We are still discussing all the possibilities
If you are still in discussion then it's obvious that he really does not want to have a dog. The only discussion can be that you are trying to persuade him to have a dog that he doesn't want.
If he was even halfway to agreeing to have a dog, then you would have one already.
Please do not bulldoze your dh into having a dog that you are convinced will help your DDs mental health. It very likely won't.
I have been there and I have done that.
My DD had/has MH problems so we had to get a cat.
The cat didn't work. I am still looking after the fecking cat.
So she wanted to go on an expensive educational course, which would solve all MH problems. We couldn't really afford it but we took a loan to pay for it. It didn't help. Then she wanted to have a gap year in Thailand, which would cure her of all ills. More money. It didn't help.
So she wanted a dog. I wouldn't have a dog. No way. I drew the line.
Which was lucky for me because she took a job 200 miles away with her (sudden) boyfriend. And I would have been left with the dog, had we got one.
I've lived with a dd with MH problems, and please believe that just getting a dog isn't going to solve any problems at all. NONE!
It's what they believe that they want and need. But we are older and wiser, aren't we? Having a puppy and young dog around is a short term distraction for a young teen.
If puppies cured MH problems then they would be available on the NHS. If your child has a MH problem, you can be absolutely sure that it wasn't caused by them never having had a dog and it won't be cured by them getting a dog.
I think you should respect your husband's feelings about not wanting a dog in the house. Not only does he not want one, but he's a bit allergic to them as well! Having a dog is a huge commitment and responsibility. Your DH does not want that commitment and responsibility. And most important of all, it will not cure your dd,
of her depression or MH problems.
Please don't discard my comments. I HAVE been there.
I still have the 15 year old cat to prove it. Long ago discarded as an emotional prop for my dd. She's a bit of a bloody nuisance really, but of course I love and care for her. ( I mean the cat, obvs)
Please don't get a dog. You will forever be hearing the cry "Well it was you who wanted the bloody thimg!"