The woman appeared by video link in the Bendigo Magistrates' Court just after 4.30pm, where the extradiction was granted.

She sobbed uncontrollably as Detective Sergeant Trent Swinton read out the details of her alleged offending.

The court heard the mother arrived at a property on Perricoota Road - adjacent to the river - in the mid to late afternoon on Thursday with her two children, aged 9 and 5.

Police allege she told her eldest son to get in the water and attempted to drown him.

Detective Sergeant Swinton told the court the younger son was screaming during the incident.

The woman then allegedly turned to the younger son, while the older son managed to struggle free before he was attacked by a dog.

The court heard the youngest son was last seen drifting face-down in the water.

The older son was "savagely mauled" by the dog and was airlifted to the Royal Children's Hospital in Melbourne. Screams were heard by people on the riverbank who did not witness the incident, the court was told.

Detective Sergeant Swinton said the woman made full admissions to her role in the incident, and told police of her "intention to kill both children".

The court also heard she allegedly told witnesses the night before that she "had to drown my babies".

No application for bail was made, and the mother was transferred into the custody of NSW Police.

She will appear in the Deniliquin Local Court on Saturday.

UPDATE 4.20pm: The woman is currently facing a Bendigo court via video link from Echuca.

NSW Police is applying for the extradition of the woman to NSW on an arrest warrant for attempted murder.

Once granted, it's expected the woman will be taken to Deniliquin where the warrant for attempted murder will be executed.

NSW Police anticipates the woman will be refused bail overnight to appear in Deniliquin Bail Court tomorrow.

UPDATE 3.40pm: A 27-year-old Deniliquin woman has been charged with attempted murder, the Riverine Herald is reporting.

She will be appearing in Bendigo court within minutes via video link from Echuca.

At which time NSW detectives will be applying for an order of extradition.

If granted the woman will be driven immediately to Deniliquin police station where she will be remanded overnight to appear before a bail registrar.

From there she is expected to be transferred to Albury.

- Riverine Herald

UPDATE 1:30pm: A mother who allegedly tried to drown her two sons in the Murray River was reportedly released from jail two months ago.

Police are in the process of extraditing the woman, 27, and preparing a charge of attempted murder.

Police are hopeful the woman will appear in Deniliquin court this afternoon.

One boy is in hospital and police searching the water for the second. 

The woman, from Deniliquin, is in hospital undergoing assessment after handing herself into police at Echuca on Thursday night. 

Fairfax Media understands police will allege she told her family yesterday that they would never see her sons, aged 5 and 9, again. 

She then allegedly travelled more than 70 kilometres from Deniliquin to a part of the Murray River near Moama, on the NSW-Victoria border. 

As she was allegedly drowning her sons, a pit bull dog belonging to a nearby resident was somehow alerted to the commotion and became involved. 

It is understood the nine-year-old boy sustained several dog bites but it allowed him to escape the water. He is in hospital recovering from his injuries. 

The five-year-old son is still missing. A search by NSW and Victoria police, SES and Maritime Rescue commenced on Thursday evening but was called off at 11pm, before being restarted at 8am on Friday.

Victorian Police divers and spotter planes are also taking part in the search. The Riverine Herald has reported police have already recovered a small T-shirt from the river.

The situation unfolded at 7pm on Thursday, when police were called Perricoota Road, Moama, where a nine-year-old boy was found with serious dog bite injuries.

He was rushed to hospital in Echuca before being transferred to Melbourne for further treatment.

Shortly after that police received information the boy's five-year-old brother was missing in the Murray River.

Sometime after 8pm Thursday, the children's mother wandered onto a property near Moama where she had a conversation with a man who then drove her to the Echuca police station, the Herald has reported.

The woman was arrested after she presented herself to Echuca police on Thursday about 10pm. 

She was admitted to hospital and received treatment for a dog bite. She has since been released.

The children were not formally in the care of their mother and were being cared for by their grandparents, the Riverine Herald has reported.

In October, police in Echuca released the woman’s photo as part of an operation to crack down on outstanding warrants. She had two warrants out for her arrest at the time. 

In a statement, Deniliquin local area commander Superintendent Paul Condon said no other parties were being sought in relation to this matter.

"The dog belongs to a local family and police and emergency services were contacted by a local resident," Superintendent Condon said.

"Contrary to rumours, the dog was not set on the child.”

UPDATE 12.10pm: NSW Police has released a statement this afternoon saying the woman was also treated for a dog bite overnight.

The woman – who is also the children’s mother – was admitted to Echuca Hospital after she presented herself to Echuca police about 10pm.

She received treatment for a dog bite and has since been released from hospital.

The woman is assisting detectives from Deniliquin Local Area Command with their inquiries and it is expected NSW Police will be applying for her extradition.

Deniliquin Local Area Commander Superintendent Paul Condon said no other parties were being sought in relation to the matter.

“The dog belongs to a local family and police and emergency services were contacted by a local resident,” Superintendent Condon said.

“Contrary to rumours, the dog was not set on the child. This has been an extremely traumatic scene for all the first responders involved and welfare support is being offered.’’

Police are urging anyone with information to call Crime Stoppers on 1800 333 000 or use the Crime Stoppers online reporting page: https://nsw.crimestoppers.com.au/ 

UPDATE 11.45am: The 27-year-old woman – and mother of the two boys – is expected to face a charge of attempted murder, the Riverine Herald is reporting.

NSW detectives, part of Strike Force Bulletin, have arrived at Echuca police station and started interviewing the 27-year-old Deniliquin woman arrested there late last night.

They are wanting to talk to her about the disappearance of her five-year-old son and the injuries to her nine-year-old son.

It is believed the children were not formally in the care of their mother at the time she collected them from Deniliquin last night and were being looked after by their grandparents.

Strike Force Bulletin was set up soon after the first reports of the incidents in Moama were made known to police.

Earlier on Thursday NSW police had issued an appeal for help in locating the woman and her children, saying they had “serious concerns”  for the welfare of the mother.

Once the woman arrived at Echuca police station around 10pm that post on the NSW police Facebook page was taken down.

It is expected the woman will be charged later today and once she appears in court NSW police will apply for extradition.

Victoria Police divers are continuing their search for the five-year-old boy, appearing to have already recovered a T-shirt.

The nine-year-old boy remains in a Melbourne hospital after being attacked by a dog on a riverside property near where his younger brother was last seen about 7pm Thursday.

The owner of the dog involved in the incident said she cannot believe her dog attacked the boy.

She said her four-year-old pit bull lives with young children and was more likely reacting to the drama going on at the edge of the river.

In her opinion she believed her dog might have actually been trying to pull the nine-year-old to safety, not attack him.

- Riverine Herald

UPDATE 10.15am: The woman remains under Victoria Police guard at Echuca Hospital this morning. 

Fairfax Media understands the woman and the two children were all related.

A police spokesperson said no other parties were being sought in relation to the incident.

She is expected to be extradited to New South Wales today.

VIDEO: Courtesy of the Riverine Herald.

EARLIER: A five-year-old boy is missing in the Murray River and a nine-year-old boy has been hospitalised with serious dog bite injuries overnight.

New South Wales and Victoria police, SES and Maritime Rescue will resume searching for the younger boy at 8am after the search was called off at 11pm on Thursday.

The search, near Moama, will also involve Victorian Police divers and airwing.

It follows police being called to Perricoota Road, Moama, at 7pm on Thursday where a nine-year-old boy was found with serious dog bite injuries.

He was taken to Echuca Hospital and transported to Melbourne for treatment.

Shortly after police received information the five-year-old boy was missing in the Murray River.

A 27-year-old woman related to the children was arrested and is assisting police with inquiries after she presented herself to Echuca police on Thursday about 10pm.

In a statement, Victoria Police confirmed they are assisting with the search.

“Victoria Police is assisting New South Wales Police with their search of the Murray River,” it said.

“Our Air Wing was doing searches from the air last night and our Search and Rescue Squad is attending this morning.”