We had concerns when DS was diagnosed shortly after birth, because we had an elderly dog. Actually, my MIL was trying to tell us we'd have to get rid of the dog -- she's not a pet person. But we asked the doctor, who didn't have issues with it. DS doesn't have allergies, has done fine with having a dog.
That dog died when DS was 3 and we weren't considering getting a new one, except DS kept insisting we bring his puppy back from the clouds <img src="i/expressions/face-icon-small-sad.gif" border="0"> So a year or so ago we adopted a new one. I wasn't ready to deal with having to housetrain a puppy, so we went thru a rescue group, who screened us, had foster "parents" and they found the right fit for us -- a younger dog, used to being around children that was trained.
My MIL is still at work trying to rid us of his beloved pet. Her response was less than stellar when we got the new dog. And last weekend she was telling us about something on the view she'd heard about dogs and germs. Sigh!