Well, I've found that people are allergic to different breeds so he might want to try meeting a bunch.
What else does he want in a dog? I would avoid "doodles" because I've actually met some that shed--I'm guessing they got more of the other parents' genes or something! It's also nearly impossible to find a decent breeder since they aren't purebred. Anyone breeding healthy, champion poodles is not going to sell their dogs to a "doodle" breeder, after all.
I'd look into Poodles, they're awesome dogs. Very fun and easy to train. Schnauzers could work but they have VERY different temperaments than the Labradors you're used to. Many of the terriers have wirey coats that don't set off allergies as much but again, very different than Labradors.
I would not get a Puli. I know Kendalle meant well because they don't shed much but that's because they have a corded coat that takes daily, difficult maintenance. Think hours a day plus days before it dries out after a bath. They are also not an easy breed to have as a "pet" and I've been told they're territorial and tricky to train. Overall, I would not recommend the Puli to any but the most dedicated folks who know they love the breed and have groomed them.
It might even be worth a shot to go a local shelter and have your father handle some of the dogs. There might even be a mystery mutt who doesn't set off his allergies
. My mom is severely allergic to cats but the occasional cat is fine...you just never know.