If you really want to use the last, final, QF747 ever, you need to make your way to BNE on a Sat evening, stay the night in an airport hotel, there are a few at Bretts Wharf.
Take a taxi or a Connexion bus to the international terminal, cannot check in online, have to appear at 6am at BNE international, show your etix and passport, check in in person, go through passport control, get into the secure zone, wait for the plane, get on, and then in SYD, go through passport control again.
Orange stickered boarding pass, means no duty free allowed to be bought.
Does not fly every day, its a flight from DFW to BNE, then to SYD.
Getting through BNE immigration is easy, not a lot of people, but the SYD side is a shocker, you need nearly the whole half Sun morning to do this, as Sun 10am or so is a very busy time at SYD international.