Northern Hemisphere fall or Southern Hemisphere fall? In other words, will you be traveling soon or next year? The weather in September can be very different than the weather in April. For example, in September and often into October, there is still a risk of avalanches on Milford Road. In the next couple of months, we may be experiencing unusually cold weather due to rare stratospheric weather event over the South Pole.
https://www.odt.co.nz/news/national/...ng-bitter-cold

Two weeks is not a lot of time. Can you change that flight from Auckland to Queenstown to Auckland to Nelson? If so, then your itinerary could look like this:

Day 1 Nelson, get over jetlag
2 Nelson-Tasman (Abel Tasman NP)
3 Punakaiki (to break up long drive)
4 FJ
5 FJ
6 Wanaka (shorter distance than to Queenstown)
7 Queenstown
8 Queenstown (all day tour to Milford Sound)
9 Queenstown
10 Aoraki Mt. Cook (because it's fabulous and not far out of your way, and I wish you could spare an extra day here)
11 Tekapo
12 Return flight to Auckland

As you can see from the above itinerary, I've left you a day or two to add to Auckland or one of your South Island destinations (such as Nelson-Tasman or Aoraki Mt. Cook). If you had more time, I'd suggest Te Anau as a base for a self drive--depending on the conditions--to Milford Road and Sound. But maybe you can do this:

Day 1 Nelson, get over jetlag
2 Nelson-Tasman (Abel Tasman NP)
3 Punakaiki (to break up long drive)
4 FJ
5 FJ
6 Queenstown or Wanaka
7 Queenstown
8 Queenstown
9 Te Anau
10 Te Anau
10 Aoraki Mt. Cook (because it's fabulous and not far out of your way, and I wish you could spare an extra day here,)
11 Tekapo
12 Return flight to Auckland

The drive from Te Anau to Aoraki Mt. Cook would take about 5 hours without stops and you will want to stop.