there is no guarantee that a labradoodle will not cause allergy problems, you would need to test the puppy around your son before you made a decision. As far as a rescue, I would not only check to see if it bothers your son's asthma- but make absolutely sure that the dog is friendly toward children. There are a lot of rescue dogs that are being re-homed because they played too rough or were aggressive with little kids. I'm not trying to discourage you though- I have two labradoodles and they are amazing, smart, sweet dogs!