Do you have a therapist or psychiatrist? If so, you could probably start by asking them about it. You should also try to find a dog trainer or behaviorist. Maybe see if there are any organizations in your area that can provide resources. Therapy dog groups might be able to help too.
Depression can be very debilitating...You will need to figure out what your biggest struggles are and how your depression disables you and affects your ability to function in public, or how it may threaten your life or safety. Then you need to figure out what can be done to help you in those instances. From there, a dog trainer can help you figure out how the dog can be trained to perform those actions, or perform similar actions.
This is an interesting article that goes over some tasks a psychiatric service dog can be trained to do. It's focused on PTSD, depression and panic disorders. http://www.iaadp.org/psd_tasks.html
Also, a final note, while you may need a service dog, your current pet may not be a good candidate for the job. It's just something to be aware of. You will be asking this dog to accompany you to a lot of different places. He has to be ok with strange situations, loud noises, obnoxious people, vehicles, machines etc. Beyond ok. He has to take it all in stride like it doesn't bother him at all. He has to be able to lay still for long periods of time if you go out to eat, or go see a movie. He has to be able to totally ignore other people, other dogs, other animals. It takes a special dog to do service work for a person.
If, with the help of your dog trainer or behaviorist, you decide your pet isn't the right dog for the job, then I'm sure they can help you pick a second dog that's more suitable.