Tough call. I wonder what the laws are regarding looking through your wallet -- can paramedics do this? Police only? Will this be a priority for them? Will anyone see it before the hospital?

Maybe a sticky on your driver's license would be more likely to be noticed. "If incapacitated please check dog ..."

An offbeat thought -- if your dog is in the car and you go into a store, can you set a timer alarm on your phone that will flash "emergency, check dog in car license xxx-xxx?"