HYPOallergenic = LESS allergenic. I hate it when people say there's no such thing. Of course there is, since hypo just means less, not absence of.
My asthmatic son and I are very allergic to cats, and we have abandoned our search for one. The closest I came to a hyperallergenic cat were Siberian cat breeders who tested their kittens for Feld 1 protein (the main culprit), once they reached a certain age, and sold them according to those levels. I recall kittens who produced the least amount of Feld 1 were priced at 8K 5 years ago, which seemed like an expensive gamble considering we might still be sensitive, and might also be allergic to other proteins.
So now we have a dog, a parrot, two gerbils, and we foster dogs...
If your daughter would like a smallish pet with soft fur, there are small dog breeds like Eskimos and such. She could also consider rabbits and chinchillas. I know it's not the same thing, but birds are delightful companions. Parrots are very high maintenance and not recommended as first pets, but she could get a budgie. Birds have highly sensitive lungs - please limit the use of non-stick pans in the kitchen, or ventilate really well when using such or harsh cleaning products or hairspray.