You can always try your hand at shooting an Osceola turkey! Bull Creek WMA is only around 25-40 minutes from Disney. Depending on traffic.
Spring gobbler is open there from March 20th through April 25th. You'll need a License, Management area permit, and a Turkey permit.
If you've never tried Hunting the Osceola it would be a perfect opportunity. Bull Creek is East of Disney on 192 that's the main road going through Kissimmee, towards Melbourne, a straight shot from Disney.
Here's a link to a map of Bull Creek:
http://myfwc.com/docs/Brochures/09-10_BullCreek.pdf