Hi there, Yun-Bin!
The two ranges you have given me lead me to an easy answer: the January date is much more appealing. The weather is, as you point out, not only free from any conditions that might spawn a hurricane, but cool, dry, and sunny.
Additionally, the crowd levels in January drop considerably after the first week of the new year. With the exception of
Marathon Weekend (next year falling January 10-13), you'll find the crowds to be manageable.
The same holds true, for the most part, for September. The weather, though, is very warm and humid, and afternoon showers are still more of a probability than a possibility.
Incidentally, a quick look at some historical weather data
(http://flhurricane.com/wiki/Hurricane_History_for_East_Central_Florida)
revealed that the last storm to affect Orlando was Hurricane Erin,
which hit in October 1995.
On select nights between September 11 and November 2, 2012, you can purchase tickets to my favorite event,
Mickey's Not-So-Scary Halloween Party. This super-fun bash might be incentive enough to make the switch to September, particularly if you love Halloween.
What a wonderful dilemma to have, right?
Have a wonderful trip!
See you later, celebrator,
-Deborah B.