You fly to NI from Australia with Air New Zealand. There are flights to/from Sydney each Friday and Monday, and from Brisbane each Saturday and Tuesday. There is also a flight from Auckland each Sunday, although this will change to a Saturday flight from June 2017.
Flight times are as follows:
To/from Brisbane – 2 hours 30 minutes
To/From Sydney – 2 hours 45 minutes
To/from Auckland – 1 hour 45 minutes
There are also several travel agencies – Burnt Pine Travel, Travelworld, and the Travelcentre – who can book flights to anywhere in the world if travel is your passion.