So now with a visa and licence in hand you can start job hunting in the pilot shortage! Other things to consider are the fact that the Oz aviation scene is closer in relation to the very thorough British/JAA aviation systems. Given that aussie pilots tend to be more theory based, one must recognise that their system is just different and it may not be to your liking. Also Australia is a large supplier of pilots to the world market (Cathay, Emirates, etc) so be fore warned there will be a large amount of pilots chasing the big jobs. The pilot shortage seems to be focused primarily in the regional market where the terms and conditions are generally worse.
The bottom line is that if you are willing to jump through the hoops, you prove to be a good guy, and you don't come with a "well that's not how we do it in America" attitude you will find a job in Oz. I love Australia, their laid back attitude, and their culture but I think it will take more than just a love of kangaroos to keep you going through the entire bureaucratic process some days.
Blue Skies,
MayFly
P.S. After 5 months I still don't have my VISA and am looking to off shore contract work in the interim. PM me if you have specific questions.