I always wanted a dog as a child but with asthma and hay fever brought on quickly I never thought I'd get one. I used to walk other people's dogs for them though and that was better for my allergies as I was outside.
I did a lot of research as an adult and ended up trying out poodles. I spoke to a breeder and she let me meet her adult poodle first and I made sure I had lots of contact with it. I was fine so when the puppies came I went and spent time with them.
I ended up getting a pup on the agreement that the breeder was more than happy to have him back at any time and keep him for herself. (She was lovely!). Her concern being that even if I wasn't allergic to the puppy hair, I could be allergic to him once his adult coat came in.
For the first few weeks I was slightly more asthmatic than usual. So I had antihistamines and used an air purifier. It never was anything other than slight though. He also was not allowed upstairs.
He's two now and I'm not allergic at all to him. He doesn't shed at all. Not a single hair.
There are a few non shedding dogs out there. As you said it's usually the dander and spit that cause allergies, so having a dog that doesn't shed helps massively. Maybe you could try to choose a few options but ask breeders if you can meet them a number of times before making a decision.
If I'm honest I'm not sure I would risk it if it had been my child that was allergic. As I said, I always was desperate for a dog as a child but I managed with walking other dogs until I was an adult and able to make the decisions myself. I would have felt awful as a child if I had been the reason for a dog being sent back to the breeder, and I'm not sure I would have been honest about how I was being affected because of that.