Squirrels can lose their fur if they have a fungal infection or if they have mange. No way to tell for sure without testing the squirrel. If it does not appear to have any scabs or red, wrinkled skin around the face and neck, it might just be an infection. They can recover from the skin infection. If it is an infection, the dog won't pick it up. If it is mange, it is possible the dog could get the mites that cause mange, but it is unlikely. Just keep the dog away from the squirrel.