As experts predict a spike in COVID-19 cases following students returning to classrooms, a new survey has forecast large numbers of infections could go undetected.

The survey found nearly one in three parents in NSW and Victoria don't plan to follow state government guidelines requiring twice weekly rapid antigen tests of school students.

While 70 per cent of parents surveyed by consultancy firm Nature said they would follow the guidelines, 15 per cent said they would only use the rapid tests if their child had symptoms.

The survey also revealed 13 per cent of parents said testing would only be done once a week or less while two per cent said they would never test their children.

Nearly 40 per cent of respondents said rapid tests provided by the government for returning to school would be saved for other occasions.

Nature's managing partner Chris Cook said the findings raised questions about the effectiveness of the scheme.

"If a third of people are not going to follow the policy correctly, it raises the question of whether it's worth doing it at all," he said.

The survey came as hundreds of protesters concerned about vaccine mandates marched on Parliament House in Canberra.

A large police presence kept the protesters, some of whom had Donald Trump and United Australia Party banners, back from the entrance to the building.

The latest vaccination figures have shown more than 40 per cent of five to 11-year-olds have received their first dose of the COVID-19 vaccine.

Health Minister Greg Hunt said the cohort was the fastest vaccinated age group in the country.

"Very significantly, some schools and some school districts are holding school-based vaccination programs and if your child hasn't been vaccinated, please allow them to be vaccinated," he told reporters on Monday.

Deputy chief medical officer Michael Kidd said while states and territories would undergo rapid testing of students, case numbers would most likely rise following a recent plateau of Omicron infections.

"With schools returning and many children doing regular rapid antigen tests, we do expect to see a rise in the number of reported cases," he said.

"This is because although infection with the Omicron variant can lead to moderate or severe illness in some people, in most people it causes mild symptoms or no symptoms at all - especially in children."

Acting federal education minister Stuart Robert said modelling indicated there would be an increase in transmission, but didn't reveal what the expected increase would be.

Monday marked the expansion of eligibility for the COVID-19 vaccine booster for 4.5 million Australians.

The time frame between second and third vaccine doses is now three months, however, some states and territories had reduced the waiting time between doses before the nationwide rules came into effect.

Opposition health spokesman Mark Butler said Australia was still well behind on the booster rollout, with less than 30 per cent having the third shot.

"It's very clear we needed those boosters in the arms of aged care residents as quickly as possible ... there are still hundreds of facilities that hadn't received their boosters."

Monday saw another 44 COVID-19 deaths across the country, with the bulk occurring in NSW, which recorded 27 fatalities.

There were eight deaths in Victoria, six in South Australia and three in Queensland.

There were more than 33,000 infections nationwide reported on Monday, which included 13,026 in NSW, 10,053 in Victoria, 7462 in Queensland, 1505 in SA, 537 in the ACT, while there were 504 and 760 in Tasmania and the NT respectively and 22 in Western Australia.