I'm allergic to dogs that moult and nearly every dog who has ever licked my wrists makes me itch.
I have friends who have minature schnauzers/labradoodles which don't moult and never had a problem with them.
I went for a poodle cross bred specifically because of allergies. I've had Millie for 11 weeks now. I did get a little itchy rash for a few days on my neck where she would muzzle me, but that has completely gone. I cuddle and get up really close to her every day and not a single allergic sneeze or wheeze.
It really was a leap of faith and I know not everyone is so lucky, but have to say its the best thing I've done.