Sounds doable but you need to check what the connecting flight options are between your origin and destination cities. Be careful of transiting the same city more than twice - it's not allowed and that might cause you problems with the flights to, within and from Australia. Also, bear in mind that premium cabin availability on QF between the US & Aus/N.Z. is very limited. You might want to look at the option of using Lan Chile from SYD or AKL to SCL then getting back to AUS on AA via DFW (that is an awfully long way to go about it though).