When she did our Parliament had to return some powers to her so that she could perform the formal functions we had asked of her. She only has these powers when she is personally in Australia and at the same time the G-G keeps all his powers. This situation has never been abused. If the G-G behaves in an unacceptable or political way, the PM can sack him immediately. Should this happen our G-G can sack the PM immediately, causing a free and fair election.
Few things can be more democratic than a free and fair election.
We have all this already. If the republicans want us to throw out our Constitution, our Crown and our flag, then they must demonstrate that they have something better with which to replace them. The republicans must show how they will appoint and dismiss an apolitical Head of State as well as dismiss a rogue PM, without causing a revolution, civil war or festering hatreds. As a congenial reminder of our remarkable constitutional development, the Queen appoints and removes our G-G and State Governors on the advice of our democratically elected PM and Premiers. This is another subtle little check and balance that would not be available in a republic.