This is the single most common mix-up on this topic, and it is worth getting right before you book. Australian citizenship and Australian permanent residence are treated differently by New Zealand.
If you are an Australian citizen
You do not need a visa and you do not need an NZeTA. Immigration New Zealand lists Australian citizens among the travellers who need neither. You still travel on your Australian passport and you still complete the traveller declaration like everyone else.
If you are an Australian permanent resident
You need an NZeTA. Permanent residence in Australia does not carry the same entry right as citizenship, and airlines check for the authority before they let you board. Apply before you travel, not at the airport.
Holding an Australian visa is not the same as holding Australian permanent residence. If you are unsure which you hold, check the grant letter from the Department of Home Affairs before you rely on it.
Travelling on to Australia afterwards
If you pass through New Zealand on your way to or from Australia, you need a current visa from the Australian government to enter Australia. New Zealand does not issue that, and an NZeTA does not stand in for it.
Source: Immigration New Zealand — New Zealand Electronic Travel Authority (NZeTA)
More on the NZeTA
Work and study
Arriving under the visa waiver lets you study for up to 3 months. It does not let you work. What counts as work is wider than most travellers expect.
Medical treatment
If the purpose of the trip is medical treatment, Immigration New Zealand requires a Medical Treatment Visitor Visa. The NZeTA does not cover it.
NZeTA or visa?
The NZeTA covers short visits from visa-waiver passports. Longer stays, work, study beyond 3 months and medical treatment need a visa instead.
Which one do I need?
Similar names, very different rules. Which scheme applies to which destination, what each one costs, and the mistakes that come from mixing them up.
Arriving in New Zealand
Your NZeTA gets you on the plane. What comes after: eGates, biosecurity, money, driving, phones, health, safety and holidays — from official sources.
eGate at the border
eGates at Auckland, Wellington, Christchurch and Queenstown take ePassports from 59 countries and territories, age 10 and over. The NZTD is still required.