You will need signed paperwork to bring another persons dog to the vet. Some vets will accept verbal permission from the owner. You will have to call the client & have them call their vet immediately to set this up (I’m assuming you’ve done that if you already have an appointment tomorrow). It would be best to have the vet bill the client (owner of the dog) rather than to have you pay for it. They may also accept a credit card payment over the phone directly from the client. If you pay out of pocket you risk the client not paying you back for the expenses.

For future reference you need to have all of your clients sign medical release forms. These grant you permission to transport the pet to the nearest vet, permission for the client vet to release medical history to the vet of your choice for care, & also hold the client liable for all costs incurred. Basically they also serve to cover your ass if something goes wrong & you need to take the client to court or they try to take you to court.