Are you a New Zealand citizen? There is a lot of information available online, for example https://www.movingtoaustralia.co.nz/australian-tax-what-you-need-to-know/
which says (amongst other useful advice):
New Zealand citizens are treated as residents for tax purposes once they complete a stay of six consecutive months in Australia (183 days).
Once you have your TFN you will pay the same tax rate as an Australian resident or citizen.
The standards the ATO use to determine your tax residency are not the same as those used by the Department of Immigration and Border Protection – for example, you could be an Australian resident for tax purposes even if you’re not an Australian citizen or permanent resident.
To understand your tax situation you first need to work out if you are an Australian or foreign resident for tax purposes. You can do that here using the ATO’s ‘Are you a resident?‘ tool.
Inform the IRD that you are Moving to Australia
New Zealand tax residence questionnaire IR886
The IR886 form tells the IRD you are leaving, or have left New Zealand so they can tell you your tax residence status and if you have any further New Zealand tax obligations. It also includes the IR597 form you can use to elect someone in New Zealand to act on your behalf.
Also, inform the IRD of your new address in Australia when you have one. It is easiest to do this online. Click here to register for the IRD’s online service, which means you can easily update your address while overseas and continue to be informed about things like student loan repayments or other tax obligations you may have.