I'm going to ask my roommate to pay half of the pet deposit that I paid for my dog
Why do you think it is okay for your roommate to pay for half of the cost for your dog's pet deposit?
I think they love the dog as their own too, so why not.
It is your pet. The pet deposit is only yours to pay, making your room mate pay for half is going to be unfair to them.
Nah, they won't mind it. They can afford it.
Having a pet is a big responsibility, you can't expect other people to take care of them for you. Just because someone can afford something isn't fair to pin extra expenses on them.