I think once you arrive in Australia, you'll need to change your mindset... for example, the AUS/NZ frequent flyer programs compared to the US ones are garbage. In a lot of cases, if you want to fly domestically within Australia, just opt for the cheap fares on Jetstar (awards QF points only on their expensive fares) or Virgin Blue (I don't like their plan, but have accumulated 6000 points). Sometimes QF comes within $10 of Virgin. You need not avail yourself to the likes of Tiger Airways- that's going too far down the gutter.
The cheap fares far outweigh any miles/points.

Many of the cheap NZ fares intra Pacific are very attractive, but don't earn points. Ditto many fares on SQ/TG- beware the booking classes- especially on V Australia.

As for Australia-USA, what can I say... either take a sleeping pill and sit in the seat for 14 hours on DL, or fly to HNL on Jetstar in starclass and get QF points.

If you'll be living in Sydney, once you see your monthy rent you probably won't be considering even the premium economy options...