If it's only two weeks you have for NZ, that's a bit light on and in only doing Auckland to CC, you'll be missing some of the best of NZ.
Five weeks for Oz or Sydney to Cairns is about the norm.
I reckon your more significant issue could be weather for whereas first two weeks of March is great for NZ, your next 5 weeks for Oz will have you picking up tail end of wet season in northern Queensland and even if you miss worst of rain itself, it will still be near 100% humidity up Cairns way - not nice, and then for asia, though you should miss rain there, you'll find it near its hottest.
If it was me, I would reverse your itinerary and start off in asia, and maybe even give both Oz and NZ a miss this time around for time downunder will only give you a superficial impression of both whereas the extra seven weeks in asia would make for a great trip, in at Singapore and do your northern trek, tacking on Vietnam and southern China to exit at Shanghai - China Eastern for back to UK.
You'll be able to take your time that little bit more in asia to get a real cultural experience and it's far cheaper travelling over there, and then at 18 you have a few years yet to consider doing working holiday visa trips for Oz and NZ.
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www.talesofasia.com and
www.attitudetravel.com you could find useful and if you still want to tack just Australia on, then travelling up through Vietnam to HK and then a ferry across to Macau and
www.flyvivamacau.com has cheap flights to Sydney and you may be able to get a reasonably priced
www.jetstar.com flight Cairns to Singapore (maybe via Bali) or an alternate could be a domestic back to Brisbane and then
www.airasia.com from the Gold Coast to KL and from there back to UK or a cheap flight back to Singapore if you can get a good deal for UK to Singapore return.
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