Another option might be to tap into the homeschool community in your area. A lot of families that choose to homeschool also have very definite ideas on the type of lifestyle they want for their family and you might find one there that could accomodate the allergy as well as care for your child throughout the primary grades at least and school her if the allergy does not go away. That way she would be more able to take care of herself and know what to touch and not touch.

The nanny route does seem like a good way to start too. Then you can bring other children in to play with your daughter instead of her having to go out.