I would be pretty certain that the legal power is easily available.
It’s the most dangerous move to make though - you at minimum risk your entire relationship between military and population
it makes you wide open to political destabilisation.
Oz has a long peaceful history of none of that crap and I honestly can’t see why dealing with a bug where people just have to stay home and read a few books for a few weeks should put that at risk.
stop them from having to go out and you should not have a problem (meaning - give them what they need - eg. Pay their bills)
As for protests - peaceful assembly - if people cannot be dissuaded- then allow it with negotiation on social distances and wearing personal protection in comparison to having a shitfight in the streets with police or worse - your military.
