Australians can all be part of a mono-culture and still have multiple ethnic origins. A Culture is not necessarily built upon race. The vast majority of Australians, far more than the US, are "white". The British maintained control of Australia much longer than they did the US, more strictly controlled immigration and set the base culture there. Even when immigrants came, they were assimilated into the existing culture.
One cultural distinction between Australia and the US is and has been gun ownership and it's origins. The US revolted against Britain. Australia did not. The US used different laws for gun ownership through out our history than what the British and later the Australians have had. Since the revolution and up to 1903, ownership of personal weapons with military application, were not only allowed, but were mandated as part of our Defense strategy. Neither Britain, nor Australia, ever had that kind of policy. Our revolution and subsequent approach to gun ownership clearly influenced and continues to influence our culture where guns are concerned and our culture diverged from Britain at the time of the Revolution, Australia diverged from Britain, if it really has, much later than the US and did not involve revolution.
Australian gun laws have never actually been the same as the US. Their gun culture is predicated upon the needs of being a frontier settlement while the US gun culture was started and is predicated upon Armed citizens being part of our National Defense.
Also, while also settled by the British, we also were settled by other Europeans seeking freedoms that could not be obtained in the European cultures, chief among them being Religious Freedom. Australia was originally settled by the British using prisoners. While some were sent to the US prior to the revolution, it was not used in the American Colonies to the extent it was used in Australia. New York used to be New Amsterdam until the British took it from the Dutch. We also got some cultural references from the French and the Spanish. Not so in Australia.