From Wiki

The rights of New Zealand citizens in Australia have been reduced by Australian government legislation over the years, most recently in 2001.

There are some eligible New Zealand citizens who are still, for most purposes, treated as Australian permanent residents. Generally, only those in Australia in the 1999-2001 period have a chance to qualify, per Form 1162

New Zealand citizens who are not "eligible" may still live, work and study freely in Australia. However, unless they apply for and obtain a permanent Australian immigration visa, they face a number of significant limitations:

• no right to claim most Centrelink (welfare) payments including any disaster relief payments.
• no pathway to Australian citizenship and the rights it confers;
• children born in Australia are not Australian citizens by birth, unless they live in Australia until age 10
• no right to sponsor relatives for residence in Australia, and sponsorship of close family members is limited to the temporary 461 visa

Due to the preferential access to the Australian labour market, it is straightforward for many New Zealanders to obtain permanent visas through general skilled or employer nominated residence. However, it can be difficult or impossible for less skilled or older (45+) New Zealanders.

New Zealand permanent residents (who are not New Zealand citizens), are not entitled to any special access to Australia and must qualify for visas like anyone else.

New Zealand citizens who want to get permanent residence have a number of options, especially if they have a "skilled" occupation. These are explained in the Australian Immigration Migration Booklets. Employer nomination (booklet 5) is most accessible, alternatively, general skilled migration (booklet 6).

Most New Zealand citizens without permanent residence - except those who are the spouse of an Australian citizen or permanent resident - are exempt from the Australian_Tax-Special_Issues that affect taxation on non-Australia source income and capital gains.