The online tool doesn't seem to show anything WLG-MEL from what I see. But there are QF flights on that route operated by Jetconnect. I think you can only book the Jetstar flights with QF numbers, I don't think the Jetconnect flights are allowed. You'll know better than I do, and there definitely are flights to SYD so worst case you can go with that, at the cost of a couple hundred miles. At any rate, you can start and end anywhere in New Zealand though, so using your required stops I would go WLG-SYD or MEL-LHR-MCT-LHR-DFW-YVR-JFK-BDA-MIA-ORD-HKG-BOM-HKG-HND-HKG-AKL. The online tool doesn't show many good F flights though, it doesn't show HKG-BOM as having F on CX? I would skip the ORD-JFK-HKG flight and just go ORD-HKG direct, that and returning to AKL instead of WLG (if you're able to do that of course) free up two segments. Maybe you could put a DFW-ANC-DFW trip in there to gain some miles, though not as much with F on that.