I just had a quick look at the QF site. There're 2 flights per day from AKL to ZQN at the moment. One is direct, the other has a quick stop at CHC, but even that has a single flight number, so only one segment regardless in this context.

the_p0et, you can fly domestic within NZ on your ONE ticket. Domestic in NZ is operated by Jetconnect, but everything is QF 'labelled'. Jetconnect is allowed on ONEs, as mentioned in the OW web site and the FAQ here.

You can try - Aus/HKG-AKL-ZQN-CHC-Aus.