K.F.
It may not be the best vacuum for allergies, etc. but the Eureka Big Boss is the best vacuum I have had in years and it was only like $45. My kids have allergies but with the exception of my daughter, they are not allergic to pets. The vacuum does a good enough job that she doesn't have a problem being in the common areas of the house and of course, the dogs aren't allowed in her room.
One thing I would recommend you considering is not totally allergy-proofing your home. The whole point of allergy shots is to introduce allergens into the child's system in a controlled way so that they can build natural immunities to the things they are allergic to. I never had allergy shots as a child and my mother worked like a demon to have a dust-free home. We had dogs but they were limited to the kitchen and basement, both of which were tiled. Consequently when I was in a "normal" environment, my allergies often went beserk. I have as an adult, done everything wrong for allergies, from not remotely being dust free to having animals including cats, a major no-no. I am still deathly allergic to cats but I have far fewer problems with my allergies with dogs and dust than I did when things were totally dust free.
I think you have to try to balance between providing the easiest environment for your child but also making sure some allergens ARE in the environment. At school, on jobs, she won't be able to control the environment like she will at home but she will still need to function there. Maybe you keep her room squeaky clean, and preferably without carpet, while the rest of the home clean but not hospital sterile clean.
