It isn't.
To begin with, the British Empire no longer exists.
Secondly, Australia became completely independent of Great Britain on 3 March 1986, when the Australia Acts came into effect. This completed a process which began with Federation in 1901.
The Australia Acts declared that Australia had the status of a Sovereign, Independent and Federal Nation. The nation still retains Elizabeth II as head of state, but her position as Australia's head of state is a completely separate position from her position as the head of state of any other country, including the UK. The Australia Act removed the ability of the British Government to make laws for Australia and removed the last legal link with the UK by abolishing the right of appeal to the judicial committee of the Privy Council.
The British Empire did not exchange kangaroos for anything in Australia.
Australia did not 'join' the British Empire, the British was the first westerners who set foot on Australia. They stuck the Union Jack down, and claimed Australia as theirs.
The British Empire
The British Empire once controlled North America, India and Australia. Many other nations were also part of the British Empire.
The British Empire - yes
Because Australia was a part of the British Empire. Because Australia was a part of the British Empire
north America The British Empire controlled an entire continent in Australia. The British Empire was the largest empire in history.
money
British Empire
Sheep
The British Empire.
Federation took place in Australia in 1901, and that was carried out with a great deal of pomp and ceremony. Australia remained a Colony of the British Empire until 1911. Australia became a Dominion of the British Empire in 1911 proclaimed by His Majesty King George V, and remained a Dominion of the British Empire until 1919. Australia did not achieve sovereign independent nationhood status until 1919 following the end of WW1. Federation was not stopped: it actually did happen. This brought about the birth of the Commonwealth Parliament of Australia remaining still firmly under British law with limited self governance until 1919.