Every Kiwi knows how to come to Australia and stay....are you not a New Zealander? if you are you do not need permanent residency, you would have received a visa at the border that allows you to stay and work!!
If you are registered with the New Zealand nursing council you fill in the form at the Australian Health Practitioners agency Australian Health Practitioner Regulation Agency - Home
and use the form for nurses registered in New Zealand.
If you are not a kiwi then you need to find an employer that is willing to give you a full time job and apply for a long term business visa or you can emigrate, which means you must be assessed by the AMNAC and then apply through immigration to be given a permanent residence visa, you will still need to be registered with AHPRA to be a Registered Nurse. Department of Immigration & Citizenship