And being part of the Commonwealth, we still have the monarch as the head of state but have Governer Generals who perform the monarchs roles when they are not about.

This is true of Australia, but having the British monarch as head of state is not a requirement for Commonwealth membership - there are a few members that have their own heads of state.

Australia didn’t rebel like those dastardly yanks. We became an independent country in 1901.

Expanding on this a bit, while Australia did become its own country in 1901 our legal system was still linked to the British one and the British parliament could legislate for Australia until the Australia Act 1986 was passed, which cut all remaining legal and legislative ties to the UK.