I think you will find Air New Zealand hold Australian Traffic Rights and at one time even operated SYD-LAX nonstop much to the annoyance of Singapore Airlines.
That would be 5th Freedom rights, which allow you to operate through a foreign country. And yes the entire world would love 5th Freedom rights to operate between Australia and the USA but that it isn't going to happen any time soon.
3rd/4th Freedom rights are what enable you to fly from A to B internationally, and my point would be that QF could be in the situation where they are using these rights bestowed on them by the Australian Government to then potentially crew the whole thing with people who don't abode or pay tax in Australia and some of whom would not even be citizens. There was a massive stink in the USA when Norwegian did this in that basically they were taking the mickey of the whole traffic rights arrangement however Norwegian did win a court case that kept them using these rights.
However it is the Australian Government that gives these rights and if you had a left of centre Australian Government get in, they may take a dim view of such arrangements