Queenstown and Christchurch flights are operated by Qantas so they may not have AVOD IFE. eoinz has previously posted that QF will attempt to schedule a AVOD IFE equipped Qantas 737 for Trans-Tasman flights but it is not guaranteed.
Auckland and Wellington flights are Jetconnect so therefore all have AVOD IFE.
For special flights such as one off flights for Wallabies games here I have noticed that they have been non-AVOD IFE equipped Qantas planes.