NZ citizens who have no medical or criminal reasons for their exclusion are granted a "special category visa" upon arrival in Australia. You declare yourself healthy and with no criminal convictions resulting in more than 12 months of incarcerated time: they run your criminal records in their computers upon arrival regardless.
You can work and live in Australia indefinitely, but you cannot become a permanent resident (or therefore citizen) unless you go subsequently through one of the other routes (family class, skilled migrant, entrepreneur, among others). You cannot collect most social benefits, even though you'll pay the same taxation rates as Australian residents. If you have children while in Australia they will not be granted Australian citizenship by birth. If there's a natural disaster, your Aussie neighbours will be eligible for much more assistance than you.
Originally Posted by
JandM
As G-Mo says, no. A NZ Resident doesn't have any more rights when going to Australia than any other foreigner. Even a NZ citizen doesn't have equal rights in Australia with Australian nationals. If you're interested in going to Australia, you need to look at the Australian Immigration website for their requirements.