Sounds pretty reasonable. Many people try to do a similar itinerary in 10 days (though I wouldn't recommend it).

I think 2 days in AKL is about right, and the bulk of your time is probably in the right place (South Island is beautiful, but takes time to get around).
Cairns in 3-4 days is good, if you are planning on diving/snorkeling the GBR it's nice to have some buffer days in case of weather, and the surrounding area, especially north of Cairns, has plenty to offer. 3 days in Sydney will give you the general feel of the place.

Honestly I wouldn't try to jam too much more in. Although if you wanted to take a couple days off the South Island and do an excursion out of AKL on the North Island, it wouldn't be a bad idea.