also to note is that it is possible to be allergic to one cat and not to another.
i have allergies to various pets, rabbits definatly... cats and dogs... depends on the pet in question.
She needs to be allergy tested to see if she is allergic to cats. No allergy to them = should not have any problems with asthma.
However, you can become allergic to them years after, I had my one cat for 10 years before any allergies and 15 years before I developed asthma.
If you do get one, try to keep it out of your daughters room so she has a good 8 hours without breathing in tons of cat dander.