Yes, your dog’s vet and food costs may be deductible! For an expense to be deductible, the IRS states it must be “ordinary and necessary” for your business. It’s possible that you have built your business with your dog as your brand which could make it “ordinary and necessary” if you frequently use him in your advertising and take him with you to events or to meet clients.
However, keep in mind that you should keep great records such as describing the events your dog attends with you, photo shoots for ads, etc. In addition, I would consider documenting the hours the dog spends performing these advertising tasks. Since I assume this dog is also a family pet, I would say that only a portion of the expenses are deductible and not 100% of expenses since the dog is not 100% for business use.
What a fun question! Congrats on your star dog! Ultimately, I’d like to explain that for certain situations there aren’t black or white answers. The best you can do is have great records and be ready to defend the question of how your dog adds value to your business and how his maintenance is an “ordinary and necessary” expense for your business. Hope my answer was helpful!