Although I look at this site fairly often, this happens to be my first post. After seeing your post, felt that I had to reply.
First, not sure about the visa working arrangements. As someone already said, guess it depends on what visa your wife is granted. But from what I know, as long as you get a tax file number, you should be ok to get "employment" on most visa types. BUT starting a business is another matter altogether. You will need advice on this.
Secondly (and the reason why I wanted to post), I also make guitars - but wouldn't call myself a luthier just yet!
I have actually registered a business, part of which will be selling custom made instruments. I haven't quite started trading yet as I'm still busy making various fixtures etc.
This isn't really the place to talk tonewoods etc, so I'm supplying an e-mail address that you can use / save for later, where we can discuss things in more detail. It's ? (I hope I'm not breaking any rules and hope I don't get told off in my first post, but this is more business related I guess!).
There is big difference in making instruments here compared to UK and I'm more than happy to advise.
All the best with whatever you decide.