QF blacks out peak flights/dates, so some specific flights will never have any award seats. You have to be flexible to take a less popular day or time of day, and you'll be fine.

The AAdvantage award rules are specific to the AA program and are identical to US domestic awards. There is no way to use a Oneworld award (the topic of this forum) for travel entirely within Australia, as the only carrier is QF. You can get a 2nd carrier if you fly SYD-AKL on LAN. Otherwise the award would have to be to/from Australia to get a 2nd carrier (CX, BA, JL). If you aren't familiar with the AA rules, they are fully described on http://www.aa.com under Aadvantage.