I think in the state response everywhere has received a little too much credit (or, arguably, criticism) for policy results that were in some cases mainly the outcome of voluntary public action, or geography, or timing. With many notable exceptions.
Australia has done nothing particularly special to stop the spread beyond locking down its borders and relying on the physical separation of people in most of our community, and the wealth and orderliness of the public on average.
The failure to protect elderly people in care homes in many places stands out like a sore thumb to me, an example of where something could have been done effectively by the state, but wasn't.