Just checked and our flight to Sydney leaves out of Bradley International terminal (not Terminal 4 where most AA flights leave from and where you'll fly into from DFW. They're next door to each other or there's the complimentary shuttle that circles all the terminals).

Warning about LAX if you claim your bag and recheck again at LAX, be careful if bags have to be rescanned. This is how Tom's bag didn't make it to FLL for FUN2 even though it was domestic flight and we were there 2 1/2 hours before departure. It has been big problem at LAX, scanners are slow and the workers don't seem to give a care whether your bag makes it or not. Lots of write ups about how desperately they need to revamp and redesign the entire scanning process here.

If time allows, I'd suggest waiting at scanning area with your bag to make sure it makes it. Hopefully they do a better job in Bradley Int'l than they do in Terminal 1 (Southwest) which is a mad house.