I never even thought about hurricane season. Going Sept 8 - 16, should I be worried about weather?
Unfortunately, August and September are, historically, the worst months for hurricanes in FL.
However, we've been to WDW *during* a hurricane (Charley in '04!) and it didn't ruin our vacation at all. Disney has an incredible system for bracing for a hurricane and cleaning up afterwards.
When Charley blew through, they shut the parks early, 11AM, on the day it was supposed to arrive. They asked everyone to go back to their resorts and wait ... movies were playing non-stop on about 6 Disney resort channels to make sure there was *something* to do in the rooms. The actually hurricane arrived a 8PM and had passed over by midnight (Charley was fast-moving and that was actually good for us tourists!).
The next morning, the parks opened on time (except for AK, which suffered a LOT of tree damage and opened the following day). Inside the parks, you could have sworn the hurricane just did a little detour around!
As far as hurricanes go, I think Disney's got to be one of the safest places in the world to have to deal with one. The poor folks out in Orlando had no power for a couple days and the roof of the airport collapsed, but inside DisneyWorld everything was normal.