Three million vaccines are being distributed before the start of the school year as 2.3 million children aged five to 11 become eligible from Monday.
So far more than 73 per cent of Australians aged 12 to 15 have been fully vaccinated, taking the total proportion of the eligible population to 91 per cent double-dosed.
The Pfizer vaccine for five to 11 year olds is being distributed in orange-capped vials to differentiate it from other vaccines and will be given in two doses at least eight weeks apart.
The government is talking with another vaccine provider, Moderna, about a rollout covering six to 11 year olds.
"There are 6000 places where people can go (for a child vaccination)," the prime minister told reporters in Canberra on Monday.
"There are 835,000 vaccines in those places right now as of last Friday and more would have been added to that since then - if you can't get it from where you would normally go, know there are other places where the vaccines are on the shelves."
The head of Australia's vaccine rollout Lieutenant General John Frewen conceded he is not surprised if there are minor concerns about bookings with millions of children becoming eligible on the same day.
"There is a lot of people getting vaccines very quickly right across the country so I encourage a little bit of patience and a little bit of persistence and I have no doubt they will get access to vaccines in the week ahead," he said.
Lt Gen Frewen says the majority of more than 10,000 vaccination points are joining the rollout of the children's vaccine, encouraging parents to keep trying to find appointments amid concerns practitioners are booked out.
Royal Australian College of General Practitioners president Karen Price said it was a mixed experience from the perspective of GPs.
"From what I've heard, it's around staffing issues in the logistical supply chain. There has been lots of furloughing of transport staff," Dr Price told the ABC on Monday.
Dr Price said GPs were telling their college they had the capacity to administer more doses, with there being caps on the number of vaccines a practice can receive in a week or fortnight.
"It would have been nice to have some contingency there so a bigger dose amount could've been delivered to offset some of the patchiness of what has been going on," she said.
"We are hoping there will be another way, which has been happening in the boosters, where if you are going through your supply more quickly you can apply for increased amounts."
Mr Morrison said the booster program continued to ramp up after millions more Australians became eligible less then a week ago.
More than 60 per cent of eligible people had received their first dose before the timeframe between shots was brought forward to four months on January 4.
NSW on Monday reported 20,293 new infections from 84,333 conventional PCR lab tests, with 18 deaths recorded.
No data is available yet from rapid antigen tests.
Victoria recorded 34,808 new COVID-19 cases and two deaths from the virus, the state's health department said.
The new infections included 17,190 from rapid antigen tests and 17,618 from PCR tests, with the state now managing 161,065 active cases.
There are 818 patients in hospital, 66 more than the previous day, including 118 in ICU and 28 requiring ventilators.
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