There is a huge difference between getting a good nights sleep and driving for 13 hours, that's tiring but not a huge deal, and putting in a days activities and then heading out for that long and, in my opinion a very unsafe way to travel.
Even though traffic, overall, is lighter at night it is prime truck travel time so you are always on the road with semi's all around you. This can be very intense. I suggest just going half of it or slightly more on that first day and then proceeding on the next for a leisurely drive to WDW. Check in and rest up and be ready for the next day of park touring.
When I used to drive from Vermont I would plan on two nights in a hotel on the way. 12 hours the first day, maybe 8 the next and the third day into Orlando. I was the only driver so I wanted to make sure I wasn't too tired, not only because of safety but also because I wanted to feel good when I got to Disney, not exhausted. But that's just me.
To me 13 hours is reasonable if it is all you are doing that day, but since, in this case, it is capping the day...I would consider stopping.