Doable but it'll be a 5 continent fare (Southwest Pacific, Asia, Africa, Europe, N. America).
You might want to consider putting in as many extraneous segments to get mileage and a free trip out of it. My suggested routing:
AKL-MEL/PER-SYD-DRW-DPS-SIN-BKK-HKG-SGN-HKG-CPT/JNB-LHR-Casablanca-LHR-MAD-LHR-LAX-DFW-YYZ
You would still have an itinerary such as YYZ-JFK-LAX-AKL leftover.