I don't think you should plan on being able to cycle with any dog, whether it's an adult rescue or a puppy. I'm not sure it's something you can count on, because you would need a dog with a very specific rock-solid temperament, and the dog would need to be incredibly well socialized, and the cyclist would also need to be a very steady and predictable rider. And even then I can envision scenarios that just wouldn't be safe for anybody.

People do it and seem to have a wonderful time, and I'm a little envious of those people. But I think there is probably quite a bit of luck involved, as well as very early training and socialization, and I would really not count on this working out with a rescue dog of any breed.

My niece has a Kelpie and he's a great hiking dog. I think dogs are more suited as hiking companions than as cycling companions, in general.