It has been said that nobody can drive you crazy unless you give them the keys. That's probably true, but if ol' man winter is working away at your wits, you won't be the first the first cyclist to seek sanity cycling south to the Florida Keys.
I recommend it highly. I did two January trips from Raleigh, North Carolina to Key West, Florida years ago, with a buddy. We had the luxury of nice touring bikes with full fenders, lights etc.. We carried No Panniers whatsoever. On the first trip, days one and two saw us through a sleet storm, and I don't believe the temperature ever got above freeing until day three. Not my favorite conditions, but with head-to-toe raingear and stylish gallon-sized zip-lock bags duct taped over both feet and hands, we more than doubled our first days mileage--from 65 to 140 miles--even with the short winter days.
I must admit I have done lightly loaded trips before in remote areas without camping gear where I was pressing for an overnight hotel--in retrospect, I feel like that was a mistake. Often the Inn would be out of easy reach at the end of the day (very good and redundant lights are always a good idea when you ride with me) or simply full. Even back then, I would rarely consider a long trip like this without some emergency camping gear, yet this was one of those times. The weather was horrible for camping, as the rain never stopped until the day we reached Florida proper.
While we did not stay in a tent on these trips, we did carry one and were prepared to use it. Because we were changing climates as we rode south, and we intended on exploring Key West for a few days upon arrival, we shipped season-appropriate clothing and some supplies to the Homestead, FL bus station. We arrived at the station after they had closed for the day, and made the pleasure of their acquaintance when they unlocked the door the next morning. We exchanged longs for shorts, winter for summer, and sent the winter clothes homeward-bound in the same box via Greyhound.
Bike theft is a problem anywhere, and bikes priced well into four digits USD are not unusual nowadays. Locking it where you can keep and eye on it, and asking shopkeepers, waitstaff and others to "please keep an eye on it" while you attend to bodily functions will go a long way (It's nice to travel with a pal sometimes). I have found when exploring a new place that a local bike shop will typically be glad to store your bike for a few hours. I always buy supplies when visiting a local shop, as a practical token of good-will.
The biggest threat to your bike in the Keys is salt air and salty/sandy soil. Keep your bike clean, and wash it with soap, fresh water and a "brush" often--maybe a couple of times per week, with an immediate (do not wait) disassembly and thorough cleaning upon your return. UV rays can damage exposed carbon fiber clear epoxy resin causing it to flake off exposing the structure to moisture and eventual delamination. Before departure, clean the frame well and touch up any gaps in the epoxy coating (some are painted). After drying for a couple of days, wax the frame very well and enjoy!
Carrying your Gear: I usually toe-strap bagged tent poles (and pegs) to the frame. It allows much flexibility in placement of the tent. I will that say that, while people do this all the time, tying gear to the bars really can interfere with hand placement (i.e.: comfort), and STI gear levers usually get in the way. Much better to use a good bar bag for this. Sometime using longer cables on the STI brifters will allow room for a bigger bag.
Actual frame size matters. A small frame has little room for big bags, front or rear, sadly. Some people think it is too big, but I use (and sell in our shop) the Carradice Camper saddle-rear mounted bag. A big bag like this is easier to load, and saves lots of time when setting up and breaking camp. Some of their other seatpost bags are also generously sized and remove quickly as well. Bring a good sleeping pad for the Keys; the campsites I found are on coral rock and very firm.
Our website has links and articles on ultralight touring and camping that might be helpful in your planning. Enjoy your trip, and I hope the wind and weather are favorable.