Premier Annastacia Palaszcuk has thanked 1000 families who went into isolation after a 13-year-old schoolgirl from St Thomas More College tested positive on Friday.

She said those families were keeping Queenslanders safe and she's "a lot more comfortable" the state might avoid another lockdown.

"Fingers crossed it's all looking good at the moment."

The 13-year-old girl's immediate family members have also tested positive for the virus. Two fellow students were added to the list on Monday.

Chief Health Officer Jeannette Young believes the newest cases are low risk because the entire school community and their households were ordered into isolation as soon as the girl's infection emerged.

One of Monday's cases spent a short time infections in the community before starting home quarantine so new exposure sites have been listed.

"But I'm fairly confident that cluster is in hand," Dr Young said, and lifted visitor restrictions on hospitals, aged care, residential disability care and prisons in southern Brisbane.

The two students are aged 15 and are "reasonably well" in the care of their parents at home, Dr Young said.

There's still concern about a number of truck drivers who've recently been in Queensland while infectious but the premier said it was impractical to test the thousands of truckies crossing the border each day.

"You can image the traffic jams that we would have," she said.

State and territory ministers have been tasked by national cabinet to look at the problem, including whether rapid testing might help.

Ms Palaszczuk said even that might not be practical but at this stage, all options should remain on the table.

Meanwhile, a police investigation is continuing in relation to the 13-year-old schoolgirl's infection.

She was infected by a visitor from NSW who was at her father's house when she went there to celebrate Father's Day.

Authorities have previously said the man entered Queensland with two others on September 5 and that they had the correct border passes.

On Monday, Deputy Police Deputy Commissioner Steve Gollschewski said investigations were continuing and officers are in the process of obtaining "other documents".

"We'll pull all the passes they did have," he said. Officers would consider factors including conditions on authorities to enter Queensland.

The new student cases emerged as Queensland opened up vaccinations for children aged 12 to 15, who can now book in for their shots.

The Queensland-NSW border bubble arrangements resumed at 1am on Monday, allowing essential workers and students in a select number of local government areas, including Tweed Shire, to cross the border.

But they're only allowed to cross for very specific reasons, including for essential work that can't be done from home, for school, healthcare and caring for vulnerable people. And they must have had at least one dose of a vaccine.

Mr Gollschewski said delays at the border had been minimal and some people had been turned away because they did not satisfy entry requirements.

"It's not a completely free travel bubble. If you don't have the right paper work and the right passes, our officers will turn you around."

Australian Associated Press