We were also in September this year and twice before. The rain isn't a heck of a lot different from June-August, maybe a little variation. You can get a hurricane, but that's not exactly an everyday occurance. We've never seen anything longer than the hour-long splash, followed by sun. We've always found the daily shower an extra to take advantage of. It cools things down, and if you have rain gear (the standard five buck Disney poncho is great), take advantge of the people waiting out the rain: walk through it and walk-on your next attraction. And look for rainbows, they're spectacular.
We like September because it's still hot. Some don't. When we were going in late October/early November, we found the occasional 50 degree night and 60 degree day a bit of a bummer. It didn't feel like Florida. However, some go BECAUSE it's cooler then. You have to decide that. Assume you'll see temps in the high 80's to low 90's. And it is humid (thus the afternoon showers).
All in all, I think September's the best month to be in Disney: a little less warm than July, and no crowds.
Good luck!
Pat