You could book a private driver in advance, but I think you will be fine by tain. The journey takes about 2 and a half hours. Try to get a train with only 1 change. London Victoria would perhaps be the easiest. You can check the timetables & journeys here.
Input Dover Priory and Gatwick Airport & your date & look for the trains with 1 change only. (You can get a slighly quicker journey if you are prepared to change a couple of times, but with luggage it will probably be easier with just one.)You will probably need a taxi from the cruise terminal to the station but it isn't far.