I used to work in a vet clinic and there would have been no extra room to be able to set aside as a private room. Even the office had a window that you could see in (and two doors!). I wouldn't be comfortable expressing in the toilet/bathroom, so I'm guessing if I had been in that situation I would have been using a spare consultation room and putting a privacy sign on the door when I was in there. A plus would be that that particular room had a mini-couch in there because the room was also used as a grieving room for euthanasias, so at least the seat would be comfy. Oh and there was a bar fridge in there too.