I'm only in a rush because I'm going to Australia in November and want to do some flying over there. Not the end of the world if I don't have my licence but it would have been nice.
What I've heard about Australia security procedures is that the process to get your foreign license validated there to fly on an AUS-registered airplane, is very, very involved and may take three months in total.
So for all practical purposes you probably will not be able to fly on your own, but only when accompanied by an Australian pilot who will formally be PIC. For that you don't need a license yourself.