I know Poodles and Schnauzers don't shed, but I believe shih tzu and maltese do some...not positive on that though.

However, with a breed like that, they may not shed but their hair grows profusely and requires a lot of grooming.

Schnauzers! They dont shed and have no oder to them
Not with my dogs...Reggie and Smokey always stink. Nebo's the one who always smells nice and has no "doggy odor." lol

There's also some hairless breeds.

However, you may want to find somebody with a breed of dog like that and be around them to find out if the dog still would bother your allergies.