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.
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.