Payload is listed on every 2006+ modey year vehicle in North America. Note what is listed on this sticker mounted on the driver's door where mine says 2051:
2007.5-2010 6.0L trucks have tow ratings 9500-10500 for 3.73 axle, and about 2500 pounds more for 4.10 axle. The 6-spd is wonderful. Use tow/haul mode. I like to also use M5 to limit never using 6th gear while towing, but you do lose the engine grade braking functionality in Manual Mode.
That's a good truck that will comfortably tow that TT. I tow about 2k lighter very easily at 65-70mph most of the time. It can hold 65mph up any interstate hill in 3rd gear if desired.
One note: the 6.5' bed trucks have a 26 gallon fuel tanks prior to 2011. That makes towing range about 150-200 miles.