I have the same problem and have had many unpleasant arguments with my husband about having the dog. We did get a dog when my son was 5 and they are the best of friends. I believe having a pet teaches empathy, responsibility, understanding, unconditional love.... I would find articles that reinforce the positives of having a pet for your husband to read, one study shows people who have pets live an average of 7 years more than those that don't. Have rules you can both can abide by, I want the dog in the house and am fine with him sleeping in my sons room but at my husbands request we don't let the dog on furniture or eat off of household dishes, easy requests.
I am really amazed at how many responses you received saying not to get the dog because it may affect your marriage or your husband will leave, if your relationship is so fragile a dog would end it there are other problems, also amazed that none of the responses said your wishes should be respected by your husband also, work together on this and I'm sure you can have the dog and a great marriage! Also having a pet is not really spoiling your child like giving them every toy they want. There truly is incredible benefits for your daughter and your family having a dog. Although my husband doesn't particularly like having a dog he completely appreciates the relationship our son now has with the dog and my husband doesn't complain about having the dog, albeit my son and I do all the work with the dog, but we aren't complaining, just having fun. We have a wonderful golden retriever, be sure and pick out a good family dog.
This isn't a choice between dad and dog, this is adding more relationships to your daughters life that she will learn from and if your husband understand the benefits I would hope he would see the positives instead of just the negatives.
Lay out the groundwork that works for you and your husband but I would stick to having a pet for your daughter, it is a relationship that lasts a lifetime.