OK, don't kill me out here with this one. Truck has a 9600 tow rating (2013 5.3 Silverado). Trailer weighs 7550 dry. Add another 1000 for cargo (That number is a little high but better more than less)...
I'm with the group that suggest it could be done for a short trip, but what you have planned will stress everything including you the driver. You will be beat at the end of each day and as a result won't enjoy the trip.