Chances are that QFi can never be profitable when in competition with Asian and ME airlines. So if you are Qantas use your great brand name to sell tickets under code share as you suggest and focus on domestic and the small number of routes where you can make money and stop trying to show off by flying to LHR.
The North American carriers are all second rate so hit that market hard where you stand a chance of competing and where the brand name is held in high regard and where you will be the sole Oneworld carrier. LAX, YVR, DFW, HNL, maybe SFO and JFK.
It has become quite apparent during my travels that there are some destinations which QF could have a lot of potential with but are taking for granted. For example, Canada. I have met so many Canadians who want to come to Australia but can't afford to come directly because the only airline who flies direct is Air Canada, and they are too expensive and not a great airline. And of course, there are a LOT of Australians who want to go to Canada as well!
IMHO QF could do very well if they flew to, say, Vancouver, because:
-there are a lot of Canadians who want to come to Australia, and vice versa
-those Canadians aren't just going to want to visit Sydney and then go home, they'll want to visit other places, meaning they will also use QF domestic, presumably
-the current benchmark in terms of fare prices is very high
-the only competition (Air Canada) has an inferior product
-the prestige of Qantas, which many North Americans perceive as a quality airline
-gives QF customers another alternative to transiting through LAX