Australia is one of the better remaining markets for GPUs, especially if you can fly Mon/Tue/Wed on each TPAC sector. UA serves SYD-SFO/LAX/IAH and MEL-SFO/LAX on its own metal, plus the option of connecting to AKL-SFO after a SYD-AKL on NZ which I have always found to be a pleasant flight. SYD-SFO is probably the hardest to clear, but I have seen PZ space at times on all routes, and I would recommend looking for it.
W fares are consistently in the $1,600 to $2,200 range, with cheaper G/K fares crashing downwards recently (I've seen $699 r/t) as a number of new entrants have led to a heavy oversupply of seats US to Australia. In some cases it can be close to equal to just use a miles+cash upgrade instead. Don't fly during high season (13-Dec-19 to 09-Jan-20 this year) as it's ruinously expensive.
If you need to travel within Australia domestically, there is no way to do it on Star Alliance. BA and AA offer good redemptions on QF metal (10k Y and 20k J anywhere in Oz -- BA might have gone up I'm not up-to-date on the Avios devaluation). I have flown both VA and QF and they both seem fine, although domestic sectors on long trips rarely stand out to me
A fun fact.. SYD-MEL is one of the busiest routes in the world and is served nearly every 15 minutes from 6am to 10pm by QF alone.