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moomin_1975
I would first choose an alliance with which you'll mainly fly, and then narrow down a frequent flyer program (FFP) within that alliance. Also do not forget about Virgin Blue, the (mainly) domestic airline which is not part of any alliance. While the FFP is new (no status levels yet), it is has a couple of international partners (Emirates and Malaysian) and expected to add more - thus increasing its value over time. Virgin Blue is often cheaper than Qantas for domestic flights.
Both one world and star alliance serve well Australia, Pacific and Asia region - albeit each with some gaps. Sky team is not helpful in this part of the world.
Star alliance has no airline within Australia, and to get between Australia and northern asia you need to transit through Singapore (SIN), Bangkok (BKK) or Auckland (AKL). There are plenty of options to europe (Singapore Thai United and Air New Zealand) and good coverage in the south pacific.
One world has Qantas in Australia, and Cathay Pacific in Asia. But limited coverage within southern asia (okay if you want to fly somewhere Qantas flies to but otherwise not so good) and pacific islands. Qantas and American both partner with Air Pacific and Air Tahiti Nui so some miles can be earned or burned visiting some of the pacific islands.
In narrowing down a FFP consider what you want out of it. Do you mainly want status benefits (eg lounge access), award flights or upgrades? Will you be able to earn much from credit card earn (only some programs have linked cards for someone based in Australia)? Once you've identified some of these factors, we can help you with suggestions and ideas.