Given recent changes to the policy around Lounge Access, you may potentially get turned down by AirNZ for access in Sydney. The thread on this is here with all the various discussion on this:
Denied Lounge Access without *G on Ticket
With that in mind though, if AirNZ turns you down, the Singapore Airlines Lounge is right next door to the AirNZ one. In my opinion the Singapore lounge typically has better food and is less crowded (it's also far better than the KF lounges at Changi). They will not have any issue with granting you access if you present your KF*G card despite it not being on the ticket.