I can see it from both sides. Not having a dog would be a deal breaker for me. I cannot physically live without a dog or three.
DH is not fond of any animal.
He must've mentioned not liking the dog I had when I met him to my dad because I walked in on my Dad telling DH to walk away before things got serious if he couldn't handle living with lots of pets. I'd warned him the same. When he bought a house and filled it with expensive flooring and furniture (against my advice) I warned him that my pets (I had two cats and one dog at the time) would have to be welcome in that house or I would not move into it with him. I also made it very clear that my pets mean a hell of a lot more to me than his fancy dining table and would continue to live with us regardless of any accidental damage of aforementioned expensive furniture and flooring.
In my eyes he had plenty of forewarning and could and should have walked away if he truely couldn't live with dogs. He didn't. Therefore he is unreasonable to expect me to not have dogs. Thus when mine passed away shortly before we moved in I was straight to the pound despite his protests. We had a lot of trouble with my new and problematic dog biting him and pissing up his freshly plastered walls. The dog still stayed (and is now trained and no longer bites dh unfortunately or pisses in the house)
With him not being fully on board any problem caused by the animals is always magnified and thrown back in my face. Even when it is the rescue puppy he insisted on keeping howling at 5am it's still my fault 
In normal circumstances I would say that you would BU to bring in a dog without your DH being on board fully but it would depend on whether pets had been discussed prior to you becoming involved as in my case.
I can't understand why couples don't discuss pets etc before becoming serious with each other, but then to me, having a dog is as much a need as having a child.
They are a massive commitment both financially (my parents recently paid £60 for kenelling their two dogs just for one night away) and time wise. They can wreak havoc on a normally tidy and quiet household. They can suddenly develop a fear of being alone and howl constantly, all night long (I'm looking at you whippy) or they can decide they now know how to open doors and their bed on the stairs is not as comfy as your bed (Yup, looking at you Devil Dog)
Most breeds still love walking in torrential rain and when you are ill. Or when your dc are ill.
Dog hair becomes the latest condiment and will be found in a cupboard or on a plate near you. It even somehow ends up in unopened jars of pasta sauce.
Doing it all alone is hard. Being blamed and responsible for any scratched flooring or knocked over vase is hard and expensive. And you would be alone if you went over DH's head and got a dog anyway. It would be unfair of you to expect him to help with something he didn't want.
Saying that if he is not even willing to sit and discuss his concerns with you then he is being slightly childish but for some owning dogs is as much of a dealbreaker as not owning them is to me.
Maybe you could help out a local rescue with walking or volunteer for The Cinnamon Trust to help fill the dog shaped gap.