No real need to worry about mileage, though, as your itinerary will fit nicely into the 4001-9000 mile OW award (60/80 for Y/J, no sense in taking F, I think) and I can't see a way to make it shorter. Pretty much any order will work although if you want to see both MEL and SYD, you could do MEL-PER-ASP-CNS-SYD-AKL on QF/LA. By the way, if you don't find any availability on LA for dates that work for you, you could do Australia-AKL via HKG for no additional miles as long as you don't stopover in HKG. It would be far out of your way, but perhaps not to unpleasant in J...

Michael