Call the AA Round The World Desk on 800-247-3247. This ticket is also known as a "Oneworld Visit Australia and New Zealand Pass" and they should be able to ticket it. I think it was marketed as a Boomerang Pass (not surprisingly given its less-than-catchy other name) but there is nothing in the starfile I have that says it is not eligible in connection with travel to/from the USA.

Looking at the starfile it is LOZPAS* with the * being A, B or C depending on the (distance) Zone you are flying. If you get no love from the AA desk, come back here for some more details.

The only real trick is that JQ (JetStar) flights are not eligible, nor are QF codeshares operated by JQ. The locals can tell you more about which flights to your destinations are operated by JQ and which ones are QF.