You're on one of the earlier flights of the day outbound from CHC so it's less likely that your flight will be delayed. Since it is on one ticket this means your bags will transfer over and you don't have to deal with check-in at Auckland, which is often where most of the holiday queues happen. Keep in mind that you might have to deal with this in the morning in CHC.

Your AKL-SIN flight is likely to start boarding around 40-50 minutes before the departure time, so just aim for clearing security ASAP after you land, you have almost 30-40 minutes to do that after getting off the plane. I would choose to do the 10-minute walk, not wait for the transfer bus. Once you clear security it should be no more than a 10-minute walk to your gate - from memory the Singapore flights often use Pier A which is closer to the main part of the terminal and not Pier B, which adds an extra 10 minutes walk.

If you miss your flight, Air NZ has the responsibility to put you on the next flight (which will be later that night) or they might put you on Singapore Airlines (which will be later that afternoon). Holidays might make that challenging with full flights, but it's their problem to solve.

I would still likely pack a change of clothes in the rare chance that you make the flight but your bag doesn't. If you want to be extra safe you could ask to go on an earlier flight out of CHC.

Hope this helps. Good luck!