Sorry I can't comment on exactly what to do, but I've converted the other way (USA - AUS) and feel fairly confident in saying that you should be in business pretty quickly.
You'll find that the FAA (
www.faa.gov) are helpful and common-sense, at least by CASA standards. Best to drop them a line or call them when you get over there and they'll be able to give you the complete run-down.
Most likely, you'll have to sit a knowledge exam (decidedly different to CASA - it's computer based but shorter and a single exam). They may give you credit on this like CASA do and only require an air law/regs exam for conversions. Then no doubt you'll have to do a flight test with an examiner. Again, decidedly less stressworthy than an AUS test.
Best sources of info:
First get yourself a FAR/AIM. It's a paperback book printed each year that contains the bulk of USA air law. You can pick them up in Australia from some pilot shops.
Many pilots self train (theory wise) in the US, and there are a number of CD/DVD based study programs you can purchase. See
www.sportys.com/pilotshop for one of the USA's biggest online pilot shops. ASA and other companies have some reasonably priced video lessons and study materials.
After that it's up to you with the FAA and the local flight school. Again, I think you'll find it generally much easier to get airborne over there than the other way around. More VORs than you can poke a stick at, and lots more aerodromes. Tonnes of radar coverage and controllers are generally happy to give VFR fligh following, of that's your operation.
Good luck!!!
Icarus