If the other adult isn't OK with getting an animal then you really shouldn't do it.
DH has two cats that I reluctantly agreed to because I knew it would make him (and the children) happy. BUT however much I dislike cats, I was still prepared to look after them, clean up the eviscerated mice and birds that appear from time to time, deal with their litter if it turned out that they had upset stomachs, and give them affection so that they became well-adjusted members of our family. I don't like them still, 5 years on, but they're part of our family so I tolerate them.
Similarly, I got a puppy just about two years ago despite DH not being keen. BUT he WAS prepared to pick up my slack, just like I did with the cats. I'm supposed to walk her every day but my physical condition has changed, meaning I can't and DH has to do it.
He's happy to, it turns out he LOVES our dog. She's a darling so everyone does, even though she's still a bit puppy-naughty and is giant and fluffy and drooly and just the best thing ever. (I love her so much, even though she's a total dick sometimes.)
My point is this: even if you promise and plan to be the person who does everything for the dog, the situation can change very quickly. If your DH isn't onboard then that's an easy route to resentment and unhappiness.