Radiofanatic First, Welcome! You have made a great decision to do this for yourself. You have plenty of time to get ready and do yourself proud.
First, I would suggest you look at the Couch to 5k program--also referred to by many as C25K. You can find info on it here.....
http://www.coolrunning.com/engine/2/2_3/181.shtml
It's good because it incorporates running/walking and will be a good way for you to ease into things and see if you might want to be a runnner, a walker or some combination of both.
Next, get yourself some appropriate gear. You don't have to spend a ton of money, but you need some moisture wicking workout gear (even Target sells Champion brand) and most importantly-a good pair of shoes (don't skimp). For the shoes--go to a local running store and have them fit you.
Once you start training, you may want to pick a local 5k race as a goal/motivator. There are lots, and you can find one that's low-key. Consider it an experiment---you can learn whether your training worked, your clothes worked. And you can learn whether you want to move onward to a longer distance.
If you decide you want to try for the half marathon, you have plenty of time to train for the one in January. People here use many different plans--Galloway, Marathoning for Mortals, Hal Higdon.
Remember to start slowly and take each day you run/walk one day at a time. It takes a while for your body to adjust to what you are doing. Some days may be good, others bad. And sometimes you may think you will NEVER be able to do the race you are training for. But you can.
As for travel to Disney....I always book my own room and try to get the best rate possible. Rack rates--via phone--are what you will get by booking now, with deeper discounts (public room-only offers) coming later in the late summer/fall. I've never thought the rates offered for runners were that great--and sometimes it's just packages.
Good luck and hope this helps.
Maura