Hi Joanne,
It's so lovely to see a question from a fellow UK resident!
My family spent Christmas and New Year at Walt Disney World last year and there really isn't a more magical time to visit.
To answer your question, the best way to get from Downtown Disney to Disney's Fort Wilderness Resort & Campground for a Holiday Sleigh Ride would be to catch a bus. I would recommend that you be at the bus stop at Downtown Disney at least an hour prior to the time of your sleigh ride.
As far as booking the
Fantasmic Dining Package goes, you are able to make advanced dining reservations up to 180 days in advance. My family actually visited Disney's Hollywood Studios and did this on Christmas Day last year and it was a lovely way to spend the day. As you will be visiting during one of the busiest times of year, I would highly recommend that you book the Dining Package which provides you with a guaranteed seat for Fantasmic and will reduce the amount of time which you will need to spend waiting in line for the show.
Please feel free to visit us again should you have any further questions.
Wishing you a magical holiday!