It is totally your call.
If it was a little bit of a drive I would casually reference to the owner the location of the vet hospital. (example: "If I remember correctly, Fido goes to the animal hospital all the way down on the other side of..." (fill in the bank). Or you can respond back with, "sure its a little bit a drive but I am sure I can work my schedule around it." Hopefully, the client will offer to throw something in for gas.
For my regular clients, I personally am okay with being flexible and not charging the client to take their pet to the vet or to a grooming appointment, to pick up thier dog food from the pet store, ect. But only when I feel that the clients are appreciative of me doing it. (I find that they do normally leave a tip to compensate me for my time, which works for me).
Now if I felt the client was not appreciative than the next time that they asked me to do something extra, I would say "sure, let me go ahead and fix our transaction so we can add that in as a cost adjustment down at the bottom."
Good Luck!