Kids under 18 do not need l.D. See site below. he may carry her inhaler with no problem. Flying should not cause her any problems. See 2nd site for regs on what may be carried on the plane.
She should be fine if she doesn t freak out and since your daughter is 16 she cant board on the plane by herself with ID. But the little one is a minor and they might take her to some sitting room where the legal guard has to come pick her up
I have asthma and I m fine flying to the sunshine state! It s a three hour flight for me, and I didn t have to use mine once!