For me, it was a few months, which my caseworker said was fairly fast. Keep in mind that this was prior to a CF dx, I actually got my disability approved on the basis of my severe asthma. At the time of approval, I was on O2 continuously and hospitalized about every few months...all respiratory related.
Keep appealing if you are denied, don't start fresh. The whole process can be very drawn out, hopefully not with you!
Keeping you in my thoughts, Jenn <img src="i/expressions/face-icon-small-smile.gif" border="0">