Well, what I'm going to tell you about allergies and dogs is completely opposite of what you've probably heard and/or read on the internet... except on the websites of responsible breeders... and here it is:
there is no such thing as
1) a completely hypoallergenic breed, mix or individual dog
2) a non-shedding dog.
In the first place 'HYPO' doesn't mean 'no.' It means 'LESS.'
Allergy friendliness varies greatly from individual dog to individual dog within the same LITTER never mind the same breed. And any one person's reaction to any one dog is just as individualistic. Yes, some breeds tend to cause less of a reaction in people with mild to moderate allergies but those with severe allergies will most likely never find a dog they can tolerate easily. As to Poodle mixes, just think about it... why would pups all inherit the allergy friendly properties from the Poodle side and none inherit the 'make your nose run and eyes itch... and throat close up' properties from the other parent? There is no way to tell how YOU are going to react except by placing you and the dog in close proximity for an extended period of time.
You're probably not going to hear this from many "hybrid" breeders, but since there ARE purebreds more easily tolerated by some people, anyone with severe allergic reactions to dogs would be better off starting there. Why? Again, think about it. Most breeders of purebreds have just that one breed around while by definition BOXERdoodle breeders (LABRAdoodle, GOLDENdoodle, WEIMERdoodle, etc'doodle breeders) have to have the other, NON allergy friendly, breed around as well. Hair and dander and saliva from that breed will be on the pups and all the other dogs. So within the initial period around the dog, your reaction could be to the other dogs and not your new puppy.
By the way, MOST people react to dander, saliva and urine rather than to hair, shed or still attached to the dog. All dogs, even hairless ones, produce dander, saliva and urine. The amount of shedding a dog does will not affect its allergy friendliness.
IF you have moderate to severe allergies, my suggestion is to try to find a breeder of Poodles or Tibetan Terriers or Soft Coated Wheatens with a puppy you do not react badly to. If you MUST have a mix, consider the Whoodle or Giant or Standard Schnoodle before anything else. Good luck to you.