For what it's worth, Emirates is a US-Australia award option, but as noted, it's... a little out of the way. But if you really want to and you're willing to shell out the miles, there's some very good (and fairly cheap) Lebanese food to be had in Dubai.
If you don't really care about how good the premium cabin is--i.e., they aren't an especially renowned airline, and they don't have lie-flat seats in business class--Fiji Airlines's award availability seems decent, and booking with them would allow you to take a stopover in Nadi. But I'd second beckoa's recommendation of Cathay Pacific, taking advantage of the stopover in HKG. I'm doing that in J on the way back from Melbourne and Singapore in February, and I'm really looking forward to it.