I'm a New Zealander who is flying from India to Auckland with a change over in Australia.
Do I need a visa?
As a New Zealand citizen, you can travel to and stay in Australia for any length of time and for any reason. Since Australia needs a name for this category of visitor, they have something called a "Special Category Visa" (SCV) which is only issued to New Zealand citizens. There is no specific paperwork associated with this visa (just the normal passenger arrival card which everybody fills out), and it's only granted upon arrival. You show up, they may or may not stamp your passport, and you walk in.
Note that some people are not eligible for the SCV, such as those who have criminal records or severe health problems. Such people must apply for a specific visitor visa instead.
To answer your implied question, no you do not need to do any advance paperwork before arriving in Australia. As long as you are holding a New Zealand passport, there should be no problems whatsoever.
For a stay in the transit area of less than 8 hours you do not need a visa. Courtesy KLM:
/ 19DEC16 / 1256 UTC
National New Zealand (NZ) /Embarkation India (IN) Transit Australia (AU) /Destination New Zealand (NZ) ALSO CHECK DESTINATION INFORMATION BELOW
VISA NOT REQUIRED.
- Nationals of New Zealand who decide to enter Australia or who have a transit time of more than 8 hours and are required to leave the transit area must apply for a Special Category Visa (SCV) when clearing immigration by presenting a valid passport and completing a passenger card.