What are the best ways to fly from Auckland to Hobart using Avios or Skyteam miles?

Good Morning from the UK.
I have been recommended to this site for relevant information and I would appreciate advice, or indeed, any particular ‘do’s or dont’s.’
In February, my wife and I are lucky enough to be able to travel for three months, primarily to visit her childhood homes in NZ and Tasmania.We fly direct into Auckland and at present back to the UK from Sydney although we could change this if necessary.
My initial question concerns the transfer between AKL and Hobart, in respect of the ‘best way’.
I have a ton of Avios and likewise KL/AF Skyteam miles, but it seems to me that Avios appears to be the way to go, not necessarily discounting paid for flights if sensible.
The London BA desk was not particularly forthcoming, maybe because I don’t have BA status anymore. I would be more than happy to call the local BA number when we arrive as that may be a better option.
However, I really would appreciate any input,

Hi mike,

A quick look found Avios flying with Qantas seem to be the way to go for this route. Couldn’t find much on Skyteam.

It seems cheaper to fly through Iberia. So you could transfer BA Avios to Iberia.