Now don't be fooled, the USA only has about 400000 sq.miles more land than Australia (not counting the great lakes).
So you can imagine what driving cross country would be like, similar to driving from Sydney to Perth, however there's no Route 66 in Australia! (not sure if that's a good thing or not).
Sounds like you are an aussie pilot hoping to come here to meet people who might help you get a job later on. The time of year you picked is the middle of winter here, it's also when airfares between the US and Australia are highest because northerners are heading down under for some sun. I would suggest making your trip in the summer time when companies are hiring pilots and airfares are cheaper.
I would suggest visiting one of the flight schools in Southern California and getting all the latest details on license conversion and TSA requirements for foreigners to train as pilots in the USA.
If you make it to Chicago pm me and I'll show you around.