G'day Messenger,
Firstly I'll make the assumption that you're an experienced BA with good BA skills (a la BABOK as Adrian mentioned). Perhaps you are a generalist with multi industry experience or you have experience in a particular vertical market. You'll need a relevant degree unless you have enormous amounts of particular experience in what someone needs.
I've moved country from Australia to UK to US and back to Australia so I hope I can speak with some authority. Firstly you'll probably have to take a bit of a backward step in order to get a job in Australia. It is very important here to have local experience to get hired. Don't ask me why, its just true. If you have good insurance or banking experience you'll get more money and it will be easier to find work.
The next thing to consider is the relative strength of the currencies. The AUD has risen about 50% against the greenback in the last few years so you may end up with a pay rise even after excepting a lower job. Which is good. The market for BA's in Australia since February is booming. So now is a good time to come.
Next thing is the cost of living because more money is no use if it costs more to live anyway. I think the US is probably a bit cheaper than Australia at the moment - depends on where you live of course. A house in Sydney in striking distance of town with three bedrooms probably starts at $600 per week but I'm not really sure about that cause I don't rent. In my experience what costs $AUD1 costs GBP1 or $US1. Melbourne and Sydney have the best work opportunities but are more expensive to live in.
You'll need to be sponsored by a local firm unless you're married to an Aussie or have some other connection. Don't know how easy or hard that is cause as an Aussie its obviously something I've never looked at.
Dave mentioned Prince2 and PMP which are both widely used in Australia. Prince2 and variations of it are more commonly used in larger more bureaucratic firms like insurance companies (including the one I work in). Neither are important skills for a BA to know - as long as you get the difference between waterfall, iterative, agile.
Skills in high demand are UML / use cases (sustained demand for this), agile is becoming huge (in terms of demand rather than successful use thereof), financial services (insurance, banking), etc.
Next steps:
1. check out the web site it.seek.com.au which is the major job board in Australia. This will give you an idea of what you're worth here. Lots of jobs will specify permanent residents only so if its possible see if you can get a transfer with your company in the US?
2. work out your visa status and plan for what you need to do.
3. get on the web and try to work out where you want to live - might depend a lot on the jobs
4. Moving country is hard. Don't underestimate how hard it will be.
I always think that moving country is about life style so I strongly recommend you aim for that and then work out what job you can get.
Post more specific questions if you wish.
Kimbo
P.S. I'm in Sydney btw.