Yes. When a New Zealand citizen enters Australia on their New Zealand passport, they are automatically assigned a Special Category Visa (SCV). The Special Category visa (subclass 444) is a temporary visa allowing a New Zealand citizen stay and work in Australia as long as they remain a citizen of New Zealand.
For New Zealand citizens who arrived in Australia prior to 1990 and who have not travelled outside of Australia since, there may be difficulty in verifying your visa details. If this applies to you, please follow the information available on the Department of Home Affairs website, that will assist you in getting an electronic record created and relevant visa granted.
As a New Zealand citizen, to verify your Right to Work with Certsy, you simply need to provide the details of your current New Zealand passport.