No worry about mis connecting flight. You need to collect your checked bagage too as mentioned before. Thé checkin domestic bag is on the right side when you go out from custom of international flight. But if you go out and the next domestic flight to Wellington is in less 1 hour. You cannot deposit ur checkin bagage directly from the international terminal. You need to walk with your bagages to the domestic terminal (10 mn) and check them in.
its my case because my friend had something to declare and tooks more time. When we tried to check in the bagage on the air NZ drop bagage of international terminal the system said that the flight is on 50 mn you need to brig them by ur own to domestic terminal
good long flight