Chief Medical Officer Paul Kelly said the community cases were a stark reminder not to wait for a jab.
Professor Kelly warned Australia's strong track record containing coronavirus could come unstuck very quickly, particularly with the onset of winter.
"Please don't hesitate to get your vaccine," he told reporters in Canberra on Monday.
Professor Kelly has written to all GPs with the latest advice on vaccine side-effects.
About 3.6 million doses of coronavirus vaccines have so far been administered across the country, through a mix of AstraZeneca and Pfizer jabs.
The number of vaccinated disability care residents has been revised up to 5888 doses from fewer than 1000 a week ago..
The overall national number is far short of what the government was hoping for, due in large part to supply issues, but the rollout could soon receive a shot in the arm.
The government is promising two million doses of Pfizer will arrive in Australia each week from the start of October. This could see every Australian who wants protection from COVID-19 fully immunised by the end of this year.
Cabinet minister Simon Birmingham said that was the government's hope but stopped short of making a firm commitment.
"There have been many uncertainties in the vaccine rollout to date and we need to continue to be honest about the fact we can't control every aspect of global supply," he said.
There are fears the rollout has been hampered by complacency and vaccine hesitancy, particularly in relation to the AstraZeneca jab. Senator Birmingham is urging people not to wait for alternative vaccines to arrive.
"Australians aged over 50 who have concerns or hesitancy should sit down and talk to their GP," he said.
Meanwhile, Scott Morrison faces stiff opposition on plans to allow vaccinated Australians to travel between states in the event of coronavirus lockdowns. The prime minister will pitch his internal passport idea at the next national cabinet meeting on June 4.
Senator Simon Birmingham said the plan would give Australians greater certainty in terms of what benefits they received from being vaccinated. But the proposal would also deny freedom of movement to the many Australians who refuse to be immunised.
Premiers and chief ministers are not sold on the interstate passports and neither is federal backbencher Matt Canavan, who says freedom of movement is an Australian birthright.
Labor has described the passport idea as a "thought bubble".
Senator Birmingham said he was focused on keeping domestic borders open rather than responding to closures.
"First and foremost, I want to make sure we keep the borders open by keeping COVID-19 suppressed," he said.
"That is the priority, to make sure the states and territories have no excuse or reason to close those borders.
"It's not unreasonable though to be talking through with the states and territories whether or not those vaccinated Australians are able to move more freely or not."
Professor Kelly said it was important to look at incentives for people to get vaccinated.
NSW Premier Gladys Berejiklian is among those opposed to interstate vaccine passports. She also believes it is too early to talk about opening the international border or allowing vaccinated people to travel overseas.
Ms Berejiklian said not enough vaccinations had been distributed to start considering any such changes.