I have seen one where the leash was attached to a post sticking out diagonally fron the right chainstay. The leash was attached to the end of the post a few inches off the ground. This prevented any sidways pull by the dog affecting the steering. I think the post might have been hinged or spring mountied so that it bent backwards if the end hit the ground while turning.
When I was a child and went cycling with my mother, our dog would sometimes grab the hem of her skirt in his mouth as he ran along beside her (no leash).