Upvote:1
I can't think of a reason that you would need to actually do this. When you leave New Zealand, you must go through exit passport control. This is an immigration checkpoint where an officer inspects your passport to record your exit and ensure that you are permitted to leave (not have any outstanding warrants for your arrest, for example).
At the point you go through exit passport control, simply hand the officer the same passport (in your case, Australian) that you used to enter the country. They'll record your exit and hand it back straight away. This does not need to be the same passport you told your airline about (for example, if you are travelling to the US and needed to get an ESTA). Exit passport control is not interested in whether you have permission to enter the next country on your itinerary, that's the airline's concern.
You may have more problems in the future if you try to leave NZ on a passport other than the one you entered with.
Upvote:2
Do citizens of the other "foreign" country require visas to visit New Zealand? That could raise questions if so. And even if not, the Immigration officer might want to know why you are doing it that way.
There is no advantage to exiting with a different passport, as New Zealand does not stamp passports upon exit. So you won't get a stamp in the other passport to show you have been in NZ.
If it is an issue of entry into the destination country and airlines letting you on board, checking in is totally separate from Immigration, so you can show the foreign passport when checking in, then clear Immigration with the same passport you entered with.