Australia New Zealand and the Pacific Islands further out form the Continent will will call Australia and Oceania. You could spend a lifetime in this part of the world but we suggest you not as the culture is divided pretty much by the antipodean or aussie way which I think to me at least is quite similar to that of New Zealand and then there are the Islands like Fiji where the culture is dramatically different.
Australia is so large that some cities like Darwin in the north are closer to Bali in Indonesia than to Sydney in Australia.
Many backpackers from the UK visit Australia as its heavily advertised and popular a bit less so New Zealand after all its a bloody long way !