Marketing to specific group of clients

I am starting my company which will offer a veterinarian to home sit beloved pets, especially those with special medical needs. Because of the experience, education and knowledge a veterinarian has to offer, this service is way above the routine pet-sitter and therefore may be out of the financial range of some.

How do I market to those select pet owners? I feel Facebook is not the best way and my only other thought is Linkin but I feel I am missing more methods. Can you please advise?