In terms of the alliances, only Qantas has domestic Australian flights (that can be purchased separate to any international flight - UA has a SYD-MEL flight but can only be purchased with the international flight SYD-LAX/SFO). Virgin Blue is the 2nd main domestic airline and not affiliated with any alliance (yet - it started as a LCC but has been steadily moving to full service and thus is expected to eventually join an alliance but that may be years away from happening). Jetstar and Tiger are LCCs and won't join any alliance.

If you are travelling lots within Australia then QF is your best bet (but also the most expensive and their award program is terrible).