Not everything prescribed by a doctor is a qualified medical expense for the IRS. Publication 502 states:
Guide Dog or Other Service Animal
You can include in medical expenses the costs of buying, training, and maintaining a guide dog or other service animal to assist a visually impaired or hearing disabled person, or a person with other physical disabilities. In general, this includes any costs, such as food, grooming, and veterinary care, incurred in maintaining the health and vitality of the service animal so that it may perform its duties.
This doesn't say anything about support animals.
Further, the ADA makes an important distinction between service animals and support animals. A service animal is trained to perform one or more assistance tasks, and service animals are protected by the ADA and must be accommodated in most cases. Support animals, which provide support through their own natural behaviors but are not trained to perform an assistance task, are not protected by the ADA. (Incidentally, someone such as a hostess at a restaurant or gate agent at an airport may not ask you what your illness or disability is, but they can ask you what assistance task your animal is trained to perform.)
Based on IRS publication 502 ("physical disabilities") in combination with the ADA, I don't think you can deduct costs for a support animal as a medical expense unless the animal has been trained to perform one or more assistance tasks for you.
