How can one go about finding someone to write these letters for you?

I'm moving 7 hours away to start law school in the fall and would like to bring my 8 year old lab. It's in a neighborhood that shuns dogs, just because the entire area is taken over by students due to the size of the university and documentation would obviously help. I don't want to live further away because I hate driving (and sold my car actually) and the possibility of being late makes my throat tight.

When I'm upset I go to her. She doesn't actually 'do' things to comfort me but she helps me to keep myself stable (I think because her ears go back and she looks so worried when I'm upset). She lived with my mom while I was in college but my mom thinks it'd be really good for me to take her especially since I'll be in a new area.

I have a psychiatrist but I've never really been satisfied with her or with the others I've seen in the past. I don't actually think she'd find this idea that lovely. I found the medications ineffective and the copays really unpleasant on my just-out-of-undergrad budget. Also, since I'm moving I won't be seeing that psychiatrist anymore... there has to be some easier way to go about this than seeing her and immediately finding a new one to agree to this right after moving.