Hello Paul,
You can read my extended post on life in Baku on this website. But regarding your specific questions about the dog and work for your wife, I did not see many dogs in Baku. I lived in the Fountain Square area of the city and was close to a lovely pet shop - we had a couple of hamsters!! But in general having a dog there won't be a problem.
As for work for your wife, I would have to say that it would be well nigh impossible. And even if there were opportunities, she'd have to at least speak Russian. As I said on my blog, English is not spoken widely in Azerbaijan and it can be irritating at times.
Baku is what you make it. I personally did not like the place but, as I kept telling my wife, 'I'm only here for the money!' I left Baku last September - two years was enough! But I wish you all the best . . . Ian.