Go Daddy seem to make it more complicated than other providers to discourage you from moving.
You would need to follow these steps. https://nz.godaddy.com/help/transfer-my-domain-away-from-godaddy-3560
in addition, when requesting a UDAI code to transfer away from Godaddy they often will not give you a correct code straight away as their system generates this in the wrong format. UDAI codes must be 8 characters long. In this situation you must email Godaddy and explain that you need a valid UDAI code.
We recommend that you call Godaddy and ask for a UDAI for your domain. Explain to them that it must be an 8 digit code and may guide them on this subject as they are used to 16 digit codes. Its worth mentioning to the agent that they have to get their international team to issue the code for you.
You can always check you have a valid UDAI code at the NZ Domain Name Commission website here https://www.dnc.org.nz/udai