If you are in the New Yorki City area look into the AutoTrain.
You would leave home in the morning and have to arrive at Lorton, VA (two exits South of the Capital Beltway) by not much later than 2:30 pm (they accept arrivals up to 3:00 only). By 9:30 the next morning (and 855 miles later) you and your car are at Sanford, FL, about an hour's drive to WDW.
Same timetable on the way home.
nd you can pack your car to the gills; just be aware that anything in the car cannot be retrieved from the time you drop off the car until it is off the train.