First, let me say WELCOME to the boards. This is a great place to ask questions about solo trips, as well as the other boards being packed with questions and answers.
Next, having done several solo trips (with another coming up this year), I can honestly say that you'll have a blast doing the World solo. You have so much freedom! You get to do what you want, when you want. You can dine where you want to, when you feel like it. You can ride an attraction 5 times in a row if you want (I did this on my first day at EPCOT. Rode in the single's line at Test Track 5 times in a row)! You are not being selfish, so don't give that another thought.
Plan to stay on-property. You have WDW transportation to everything Disney, so you'll really not need a rental car (I never get one when I go solo). Mears transportation is inexpensive and not too bad. I would suggest contacting CRO and putting in a request to be close to the main building at whatever resort you are at. This makes the walk from the bus/monorail/boat a much quicker one.
Of all the times I've been solo, I have never once felt unsafe at WDW. Just use common sense and you'll be fine. Make sure to double lock your door, even if you are only going to be in it a very short time, at all times. Never answer to the door to anyone you don't know. If they claim they work for Disney ask them their name and the purpose of their visit, then call the front desk to verify why they are they. Better safe than sorry. If your room has a balcony or patio, make sure that the sliding door is securely locked. Never leave valuables out in your room. Make sure you lock them in the in-room safe.
I make up my Mousekeeping envelopes before I leave home, as well as envelopes with daily spending money for snacks and such. When I check in, I lock these in the safe with my license, airline ticket and credit card. Don't take alot of cash or credit cards with you. There are ATM's all over the place if you need quick cash. I usually put my meals on my room key, which serves as a charge card. At the end of your trip, you can either have everything put on a credit card or pay with cash. Each morning I'd take out a Mousekeeping & spending envelope for that day and leave everything else locked up.
Since you are heading down in December, I would recommend bringing a sweatshirt, long pants, a hat & gloves. When I went last year it was down right chilly some mornings and evenings. Having to run out and buy all of these in the parks or resorts can get quite expensive. Better safe than sorry.
I may be the minority here, but I did MVMCP once a few years ago and it was cute, but not worth the money I thought. I would STRONGLY recomend doing the Candlelight Processional instead. I saw this for the first time on my last trip and it was INCREDIBLE!!!! I would definitely recommend the dinner package, as this included dinner and special seating at the CP. I had dinner at the Rose & Crown (got a patio table that overlooked World Showcase -- Beautiful), then headed over to the CP. The speaker was to originally be Roy Disney, but he had to cancel and Edward James Almos replaced him and did an fantastic job. Dinner was great and the whole package was completely worth every penny.
The fireworks for MVMCP are a must to see, since they are shot off in the round. I would recommend dinner at O'Hana's about 7pm (make a PS as soon as the 120 day window comes up on one of the nights of the party, since this is a popular place to dine). Relax and enjoy your dinner (food is great), then head out to the Polynesian's main beach and grab a seat in one of the hammocks or lounge chairs and enjoy. The Electrical Water Parade is shown in front of the Polynesian's beach at 9pm nightly. Shortly afterwards they shoot off the Fantasy in the Sky Fireworks, then the party one's. You can faintly hear the music to both fireworks. This is a great vantage point to view these since the beach is directly across from the Magic Kingdom and you can see the Castle, Space Mountain and hear the railroad train. I did this on my last trip and did not feel like I missed anything.
Make sure to take some time to view the resorts at the MK & EPCOT (and the AKL) for their holiday decorations and gingerbread displays. These are really amazing to see how creative they can get. I took some pics of the display at the GF & BC, and video of the AKL, YC & BW. The decorations in the resorts are just breathtaking and themed to that resort. What I did was take a break in the afternoon on a MK day to tour the Grand Floridian, Polynesian and Wilderness Lodge (very little to look at at the Contemporary), then on an EPCOT day to tour the Beach Club, Yacht Club and Boardwalk. Their gingerbread displays were absolutely amazing!!! All of the parks are decked to the hilt with decorations and there is holiday music playing in the background everywhere.
Drop me an e-mail and I can send you some tips that I've learned on my trips.
Enjoy youself and don't forget to wear a limegreen ribbon. This is a way for Dis members to identify themselves. 
