Queensland's pre-arrival requirement has led to delays of more than four hours at Wodonga's testing site.
Hundreds of cars were turned away in the past two days at Wodonga's drive-through clinic at Gateway Lakes with capacity reached before midday.
Wodonga Upper House MP Tim Quilty labelled the need for travellers to be tested "ridiculous" as it put centres under duress which had struggled for weeks.

"It was always going to go into overload and now it has due to the demand to get tested to go to Queensland," he said.
"My sister was flying to Queensland on Boxing Day and she and her two children got tested at the same time. The kids got their results back but she didn't get hers until they were just about boarding the plane.
"It's not as if they don't have cases up there, they're just a few days behind Victoria.
"It's a complete waste of money, but it pays well with the voters and states have been doing that for ages."
Wodonga resident Jennifer Cross lined up to be tested yesterday as she had woken with symptoms on Boxing Day, but was forced to spend most of her day in the queue.
"They should set up separate testing for those who need to travel to people who have symptoms," she said.
"I'd rather be home in bed.
"I don't travel very much, but when Melbourne had its big lockdown my daughter was very sick and I didn't get to see her, which was really frustrating."
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Albury woman Cate Stevens is booked to fly from Melbourne to Queensland tomorrow morning and has a nervous wait for her result.

"I hope that the lengths that everyone is going to disrupt their holidays is worth it at the other end. I understand staffing is probably an issue but it doesn't help because they have got quite reduced timeframes," she said.
"My partner came through at 7.30 in the morning and he was coming out as I was coming in."
It was a stark contrast to testing sites north of the border at Albury Showgrounds, Lavington Sports Ground and Lavington Hall which weren't under anywhere near as much pressure.
Melburnians Piers and Gabriela Charters-Wood and their children decided to get tested in Wodonga before they arrived in Sydney and went on to Queensland.
The family departed at 6am but their trip was ground to a halt.
"I think with all of the other states, essentially, except for Queensland and WA not having that requirement to be tested, it seems a little bit ridiculous," Mr Charters-Wood said.
"It would be nice to be a federation of states rather than individual entities.
"Vaccination status should be enough."

It was Mrs Charters-Wood's 12th COVID test but she was desperate to get to the Gold Coast to meet her two-year-old nephew for the first time.
"We spent two years being told by the government to be scared of this virus, and now they're telling us to get used to it, go out there and travel, but they're still putting all these restrictions on us," she said.
Albury Wodonga Health was contacted for comment.
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