Quick point of clarification, you understand that Australia is an independent country? The way your question is worded makes it sound like it's still a part of the British Empire.

Just to clarify Australia is independent of Britain in that Britain has no control over any Australian law or aspect of its policy (domestic or foreign). They share a monarchy but the Queen's representative is appointed by the Australian government not the British one. There is an Australian republican movement and there was a referendum recently on changing to a Republic but that was is too recent for this sub reddit. The most important example of Royal interference was the dismissal of Gough Whitlam's government but that was done by the Crown in an Australian capacity not on behalf of the British government.

The origins of this model of Independence lie in the Statute of Westminster of 1929 which gave Dominions the power to amend UK legislation on their own. This has evolved into de facto independence.