It depends on what you mean by similar. There's a book by Stuart McIntyre called A Concise History of Australia, that goes into some detail about the frontier of settlement in Australia. There were major differences from the US, but they were similar insofar as there were zones of European settlement gradually pushing into areas that were populated by indigenous people.

There is also a fantastic book called Possessing the Pacific (edit: written by Stuart Banner), that compares processes of European colonisation in Australia, New Zealand, Hawaii, Tonga, Fiji, and the US and Canadian west coasts. Every case was different, but most had some equivalent of what could be called a frontier zone.