What you are asking about is a Guest Assistance Card (we call it a GAC to avoid typing so much).
As Talking Hands mentioned, GACs are given based on
needs, not diagnosis. Even if they were given on diagnosis, asthma is not a diagnosis that always causes any problems - many athletes have asthma (in fact, especially many swimmers and skaters get into sports to help their asthma), so just having it does not mean the person has a disability that requires any accomidation.
Also, the GAC doesn't act as a fastpass.
it says right on the GAC that it is "not meant to shorten or eliminate waits in line" (like a fastpass). It's not a pass, it is a
tool to let CMs know what special accomidation is needed for someone with invisible disabilities. Because the accomidations are based on
need, there is not one specific GAC. What the GAC says is different, based on the needs of the person the GAC is for.
If she has endurance needs (like can't walk long distances), it is recommended by Disney that people with endurance needs consider a wheelchair or
ecv because the amount of time/distance spent waiting in lines is much smaller than the time spent waiting in lines.
Her best net would be to use Fastpass *** much as possible. Also, in general, the earlier you can get to the park, the quieter it will be and the more you will be able to see without waiting.