any trailer fully loaded at 9800 lbs??
No and that's partly why people get in trouble. Another is looking at dry weights. The tow ratings are generally for the best case, easiest type of trailer and lowest load in the cab and TW. Frontal area is also restricted for some vehicles tow ratings. A 9000 pounds boat or flatbed car hauler will tow far easier than a 9000 pound RV.
3-week trip will add at least 1500 pounds over dry weights and probably 300 pounds to TW.
6500-ish pounds dry should be okay for the 2014 GM twins. Typically equipped crew cabs have about 1700 pounds of payload, so 900 pounds of TW should be good.