If you're willing to spend a whole bunch of money, there are hypoallergenic cats. http://www.allerca.com/. Alternately, some small dogs, like the bichon frise are hypoallergenic because they have hair instead of fur.

You should try a bunny rabbit. Rabbits can be quite affectionate and enjoy human contact. They can be litter trained and they can be trained to respond to a limited number of human commands. They are wonderful pets.

One note of caution, however. Many people get rabbits thinking of them as a larger version of a hamster or gerbil (what some people call a "disposable" pet). This is really not the case. Rabbits can live for up to 10 years, so when you get a bunny, you are in for a commitment.

I'd also encourage you to adopt a bunny rather than buy one at a pet store. Here are some links to look at.

www.rabbit.org
www.rabbitnetwork.org
www.rabbitresource.org

terriers are hair-y (not furry) dogs. there are lots of varieties of little ones in addition to what sjg mentioned.

i am allergic to pracitcally everything: dogs, cats, mildew. and i grew up on a farm. (oy.) lots of exposure to all sorts of everything.

much to my delight, i recently discovered that i am not allergic to poodles! it is sooo liberating. with a little luck, maybe that'll be the case for your daughter. i'm guessing other hair dogs (rather than fur dogs) are also hypo-allergenic.

curious to know what works for your daughter!

wheaten terriers are hypo-allergenic and really amazing dogs. they're very affectionate.

Allergy meds :)

tibetan terrier. best dog ever.