Well as long as it's still the same as it always was, there's a Kennel Master, and they know enough to take care of a lot of things without a vet.
And for all we know, he may also use homeopathy.
I wasn't referring to the hunting dogs (do they still have those?), but her personal pets, the Pembroke Welsh Corgis. I wouldn't think the Kennel Master would be in charge of them, but I could be wrong.