You don't need to convert the licence - to begin commercial training you need an ICAO PPL, which is what you have.
What you might want to do while you're there is some hours building - it's a lot cheaper in Oz than it is here. Unless of course you decide to do a full-time "integrated" course, for which there are no flying pre-requisites.
I'd also point out - in case you're considering it - that it's virtually pointless doing any commercial training in Australia as the conversions to JAA involve almost as much effort as just doing it here from scratch.