The single best move is to get your kid tested by an allergist before making any decision - you need actual data on what triggers the allergies, not just assumptions. Dog allergies come from multiple sources (dander, saliva, urine), and some people react more to certain breeds or individual dogs than others. You might find your child reacts badly to one dog but fine to another, or that the problem is manageable with the right setup.
Your skepticism about "hypoallergenic" breeds is justified. There's no such thing as a truly allergen-free dog, but some breeds do shed less and produce less dander, which can make a real difference. Poodles, Bichon Frises, and some Portuguese Water Dogs tend to be gentler on allergies - but this varies wildly from dog to dog and person to person. The allergist can sometimes help identify which breeds might work better for your specific situation.
If testing shows it's possible, you could try fostering a dog first to see how your kid actually responds in real life rather than just guessing. That way your partner gets to experience dog ownership without committing to something that turns out to be a nightmare for your child's health. If it doesn't work out, you'll know for sure rather than always wondering "what if.