The dog is not a medical expense that you can deduct as noted by @DoninGA . But, could it be a charity donation?
Maybe. You can claim a tax deduction for the cost of providing service to a charitable organization. The organization must be registered with the IRS as an exempt organization, and if the amount you claim is more than $75, you need some kind of acknowledgment from the charity that you performed a service for them (the letter does not have to specify the cost, you do that with other records.)
Expenses you can deduct are expenses directly associated with providing your service to the charity. You can deduct car mileage to and from the charity. You can probably deduct the cost of a vest or special harness for your dog, presuming that the dog is required to wear a vest that signifies they are a therapy or service animal (something I have seen from time to time). You need to keep reliable written records of your expenses in real time or near-real time. (If you guess at your expenses, and only write them down when you get an audit letter, that will usually fail the audit.)
However, you can't deduct the cost of food, water, or vet care, because those are ordinary expenses you would have even if you did not perform charity work with the dog. You can only deduct expenses that are specifically associated with providing service to the charity and would not have been incurred except for the charity service.
Whether you get any actual benefit from the charity expense deduction depends on your income, your other deductions, and various state and federal laws on charity donations.
See here for more,
https://www.irs.gov/forms-pubs/about-publication-526
