I will as I have done before recommend Minovation at Jandakot Airport in Perth. I flew there a year ago for a couple of months around Western Australia and it was simple. It involved getting the CAA to release my details to the Australian authority (CASA) and then filling in some forms when I arrived in Australia. I was flying there within 3 days. Min stokes offered lots of help (
www.minovation.com) and the guy at Perth's CASA office that seems to deal with the authorisation to fly on a UK PPL is called John Pritchard (if memory serves correctly).
If you do go over there have a great time and pick the time of year carefully... It seems June is a bit of a dodgy time regarding rain in the lower extremeties of the west coast... I reckon March would be your best bet. Let us know how you get on!
Jimmydacraw
Edit : PS : If you want any more info feel free to PM me, I still have all my PLOG's and maps and all manner of stuff from when I did it last year