Whilst they are making the domestic check-in experience more self-service (people wanted it, they didn't want to have talk to some bored person).

At AKL/WLG/CHC you will find the fully automated check-in, to the side of these check-in areas there is help desk (which has a large "Help is here" sign).

60minutes is a very tight connection, I would be out of my comfort zone doing a ZQN-CHC-SYD with a 60minute connection even on one ticket!

ZQN is prone to getting weather problems, an 30minute delay could though your plans out the door!. They may allow you to though check, but they may also refuse to being on two tickets.

What type of fare is you ZQN-CHC, if its a Flex Plus (refundable) you may want to call NZ and see if you can get a domestic add on fare for ZQN-CHC added to your PNR.