Your Pet is Not a Tax Dependent
There are many court cases that have repeatedly said your pet is not a dependent. In one case, the court concluded (a) pets could not be dependents, (b) medical expenses of pets are not tax-deductible medical expenses and (c) pets cannot allow you to claim head-if-household status.
In this case [L.J. Schoen, TC Memo. 1975-167], the Judge concluded:
Under no circumstances can a pet qualify as a dependent so as to allow a medical expense deduction for veterinarian fees.
Pet dogs or cats cannot qualify as dependents for purposes of claiming head-of-household status.
Tax Tip: According to IRS Publication 17 (Your Income Tax), medical expenses include “Guide dogs or other animals aiding the blind, deaf, and disabled.” No detail is provided so my interpretation is that the purchase price is a medical expense. Revenue Ruling 55-261 provides that medical expenses include the cost of a "seeing-eye" dog and its maintenance.