Basair's website is basair.com.au
Seem a pretty good outfit. I hired an Archer from Illawarra too, right next door at Bankstown.
There's some great flying in Australia and cost of living is half that in the US. More than 3 or 4 weeks and you've saved your airfare in accommodation bills alone.
And you can fly on your CAA medical. You'll just need an Australian Special Pilots Licence ($50 while you wait - CASA office within sight of Basair / Illawarra) which lasts as long as your home licence is current.
Airspace etc is v different though. Expect quite a long period of check-outs before they'll let you leave.