Kid with Asthma and Dog.
Asthma and Dog Breeds

The more reasonable is to ask first for medical advice, because allergy to the dog's hair and dust are very common, and buying a dog could mean to aggravate an already existing medical problem. We must think then about buying a dog from those breeds that don't shed hair in a conventional way, or one of those called "hairless", like the little Chinese Greyhound. Unfortunately, the latter is very hard to find.
kid with asthma and dog
dog for people with asthma
dog for child with asthma

Having children:
Can I have a dog?