Amish - I went out to Perth for a few weeks last year. You need to plow your way through the security documents and how to get them :
http://www.casa.gov.au/scripts/nc.dll?W ... c=PC_90101
If you've left yourself enough time then aircraft rental is a possibility after checkout with the relevant security clearances. If time is limited then the work around is to take an instructor - which is what I did. No security cards needed, though you can't go to the big airports.
The Oz aviation security checks are among the toughest in the world and leave the yanks in the shade.
Rules and R/T takes a morning to get used too. You only call the last three letters of the reg. That is, not the VH. But as I found in Perth there were several female Irish ATC's who were very patient when you didn't get it quite right.