I hate to say it, but in its proposed form I can't see this airline surviving.
There is no market for this type of operation. Air NZ has and is always looking for new routes but the linking of regional centres is not commercially viable. Even with Air NZs cost base being considerably lower than that of KRA, given they already have the infrastructure at these airports, they can't make it stack up.
Initially they will probably do ok, they will get those people that are curious, the anti Air NZers and a handful of overseas visitors but long term people are going to want convenience, frequency and reliability. I just can't see KRA being able to offer that with two aircraft on a quite a long bus service type network. What happens when the aircraft breaks down in Queesntown? The next service through there won't be for a few hours, and it's not like they can offload pax onto Air NZ or Jetstar.
With regards Whenuapai as a second airport for Auckland. It's not going to happen in the short to medium term. No one is going to stump up the millions required to provide terminal space, additional taxiways, road access, etc. that would be required to make it work. There is no reason why it can't be a joint civil/military base its just not laid out well enough to allow for separate operations. There is a lot of available land by RWY 26 but that area lacks good road access and has no apron or taxi ways.
I'm sure there probably is room for another regional airline, but this type of service is not the answer. Do what Sounds Air and GBA are doing, work into the main centres and work with Air NZ/Jetstar to provide good connections.