the important thing to be aware of is that when moving to australia is only under certain conditions will you be eligible for all the benefits/tax credits that australian's get (there was a change to the system in 2001) and there is a standdown period for 2 years for some things.
ie ... Note: The Agreement does not cover workforce age payments such as parenting payment (single or partnered), newstart allowance, sickness allowance or special benefit. People moving from New Zealand to Australia who wish to obtain these payments must be:
an Australian citizen
the holder of a permanent visa or
a protected SCV holder (generally this applies to SCV holders who were in Australia on 26 February 2001. Some other exceptions also apply).
A two-year newly arrived resident waiting period also applies to most social security payments.
New Zealanders living in Australia who do not fall into any of the above categories and are not covered by the Agreement may however qualify for Family Tax Benefit, Maternity Allowance, Maternity Immunisation Allowance or Child Care Benefit.
linky