Can two partners reach a consensus when one wants a pet and the other doesn't?

My girlfriend and I are planning to move together in the same apartment because we have been together for a while and we spend much time at the other's place and we think it's worth moving together to share the rent. The problem is that she wants to have a dog, but I don't, because I was bitten by a dog as a kid and now I am afraid of dogs. I am not as afraid as used to be, but I wouldn't live with one in the same house. We haven't talked about it much as I don't express my fears openly to women. She always told me she liked dogs and I omitted to tell her about my fear, but I didn't lie, because I find dogs cute if I see them in pictures and they are at a certain distance. I really don't want to have a dog around me, but it might not be fair if she sacrificed her wish for me. Do you think that it's a deal breaker and we should break up? Should I go to therapy to overcome my fear? Should I live in fear with a dog for a while and see if I get used to it?

Can two partners reach a consensus when one wants a pet and the other doesn't?
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