well, my dd is not asthmatic...but i am!
i first showed signs of asthma in 7th grade. my father is a pulminary physician, so he gave me albuterol inhalers. i NEVER liked them. they made my lungs feel better, but left an awful taste in my mouth and throat...and left my whole body feeling shaky.
so, for most of my young adult life, i didn't take anything. not the SMARTEST thing, but i did learn to really know my body, my lungs, my illness...and can tell long before an attack would ever happen that i needed to focus on breathing, resting, etc.
this zen method of treatement couldn't last forever though. a few years ago, i had a near attack and went in for more tests. my asthma had gotten worse. i now take singulair...and LOVE it. it is a b class drug, and i believe it is safe for children as young as 1 or 2. i rarely need an inhaler (i still have albuterol and also have pulmicort).
other things is have done to help; we bought a hepa vacuum instead of getting rid of our pets. we no longer sweep, as it sends all sort of dander into the air. oh, and i like to use rosemary and eucalyptus essential oils in the winter when my asthma is the most sensitive.
best of luck!