Has a client ever asked you to pick up their dog?

Many sitters offer a pickup service or drive to vet service for their clients and add an additional fee to the booking to cover the time and mileage. Next time you speak with the owner I would explain to them that Rover doesn't provide the home address until the booking is accepted and you need their address to best serve them. Best of luck

It appears that's approx. 5 miles distance, which wouldn't be unusual for a sitter who offers pick-up service for an additional fee. His comment that "his dog needs to go to a hospital later" definitely sounds odd though.

I wouldn't mind picking up a dog that I perceived was healthy and would be in my care. If a dog in my care needs medical attention, I'll arrange that too.

However, I would not want to transport an ill dog, who didn't know me and I didn't previously meet, to the hospital. This situation sounds weird and potentially dangerous (ill dogs may not behave as predictable as when they're healthy, especially with a stranger and he didn't disclose why his pet needs to go to the hospital - is he bleeding, vomiting, diarrhea, fleas, ticks, etc. and are you prepared for those possibilities, not to mention when you arrive, is the dog a runner/ how would you interact with the hospital, is his authorization & charge card on file with the hospital). It's not clear if he only wants you to transport his pet to the hospital as a single service (which again I wouldn't offer) or if he wants you to offer pet sitting (presumably prior to hospital transport, which doesn't make sense either, and I also wouldn't sign up for).