Hello, welcome!
I want you to know that I totally understand your concerns. My husband suffers from severe allergies and asthma. He uses his inhaler many times a day...but not because of our dogs, thank goodness!
Maureen made a good point about Poodles, and if you dont' clip them in that silly fashion, they almost look like Doodles!
I agree with the others that one of the things that make Doodles such great family pets is that they adore the family. My dogs, although they WILL spend time outside, would rather that I am out with them. It is their ritual, even at night, that I go out with them to potty...and when I come in, so do they. They really do follow me everywhere....which, of course makes a very nice pet for your daughter.
One thing that you might want to keep in mind too, is that often people are allergic to the PRODUCTS used on the dog...for instance, the shampoo, rinse, etc. Or even that these dogs, due to their coats, will pick up allergens from outside, like dust, dander from other animals they play with, pollen, etc.
So, I think (as the others have mentioned) that having your daughter spend time with a few Doodles might help you to know...and also, if you get one, someone (not your daughter, obviously) should brush it before it comes into the house every day.
What state are you in? I know that there are many of us with puppies all over the place, maybe we could arrange a visitor for your daughter...perhaps in an open space.
When we met our dogs, my husband didn't know if he would have an attack (he can't be in a room where an animal has been, even if the animal is no longer there...) so our breeder gave the puppies a bath and brought them to us in our hotel room (where we knew that my husband was not having reactions.)
After snuggling with the dogs for an hour, we took a chance...still, knowing that things could change...and we brought 2 puppies home, fully expecting to make a gift of them to our family members if it didn't work out for us.
Well, we became breeders because it worked so well that we wanted to share this lovely dog with others!
Soooo, I think it is worth a try...but find a breeder willing to work with you.
Perhaps starting with a sample of the dog's hair...and moving on from that point.
Please feel free to contact me if I can help. If you want to send a PM to me (click the PM button for private message) I will send you my phone number and we can discuss whatever you'd like.