A lot of airlines fly trans Tasman. A lot with B737 A320 type aircraft. And can be economy only. Some wide body aircraft. But not many from CNS direct - non stop to NZ.
You will not get many, or any, ff miles on Air NZ flights, so check before you buy if ff miles are a side objective.
Other wise buy on price & schedule. Check carefully if checked luggage is included: can be an add on extra. Aust-NZ (~3:00 hrs) is mass public transport: keep your expectations low.
Airlines that fly Australia (CNS* MCY* BNE OOL SYD CBR MEL ADL PER) to/from New Zealand (AKL WLG CHC DUD ZQN) (not from all airports to all airports)
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Air New Zealand (codeshares with VA) [Star Alliance] {* seasonal}
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Virgin Australia (codeshares with Air NZ) (Delta partner)
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Jetstar (owned by QF)
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Qantas (codeshares with EK) [OneWorld Alliance]
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Emirates (codeshares with QF)
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LAN (SYD AKL) [OneWorld Alliance]
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China Airlines CE (BNE SYD MEL – AKL CHC) [Skyteam Alliance]
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Singapore SQ (CBR WLG) [Star Alliance] from Sept 2016
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Air Asia D7 (OOL AKL) from March 2016
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Philippines PR (CNS AKL)