American Airlines is the first US carrier to order the 777-300ER model. Air Canada and TAM have them - only three airlines in the whole of the Americas have ordered the 777-300ER.
Story was a few weeks ago, that AA might be taking some 777-300ERs that JAL had ordered but no longer wanted. I have not read the story in detail to see if these aircraft are JAL slots, but Qantas could get some of the same planes.
If Qantas was interested in the 777-200LR aircraft, I think that aircraft would be able to do a flight from Dallas to Sydney, without the need for a stop in Brisbane. Airlines fly the 777-200LR with about 285 seats (maybe a bit less if they have Premium Economy), which is only a few less seats than a 747-400ER as used for SYD-DFW services. Perhaps 5 777-200LRs would allow Qantas to do a daily service to Dallas and keep SFO. 777-300ERs would be for Frankfurt and some London services.