I totally recommend going in September to WDW. In the past, we had usually gone in June/July/August . Last year we went the 2nd week in September and loved it. The crowds are almost non-existent (walked on almost every ride).
The weather, while unpredictable, really isn't that bad. I think it may be bad if you were standing in line or crowds or people, but that was never an issue for us. There was usually always a breeze - but since we got into attractions with ease, we were hardly ever really hot. We carried a small fan around with us, though, which did help in those instances where the heat got to us.
Be prepared for afternoon showers and such, but otherwise, this is a great time of year to visit! (and the water parks are open and also not as busy as during the summer!)