I can tell you that towing your trailer will be fine as many have said the payload will be over if the numbers you provided are correct. That said I have a 2011 Ram 1500 outdoorsman with 3.92 gears and heavy duty towing package. This added a trans cooler and the gears also have LT tires from the factory. I have a 2013 shasta revere and it weighs 6800lbs loaded ready to camp. I have towed 300 miles one way to campgrounds with absoulutely no trouble. I have a weight distribution hitch and antisway. My tongue weight is right around 850lbs loaded ready to camp. My payload on my truck is 1400lbs I forget the exact number but it is very close to that. That number is right off the sticker again I dont have it in front of me but I know its more then you are claiming yours is. Max tow is 10,500lbs. I am guessing you have either a Laramie or an outdoorsman because normally they have 3.55 gears and max tow of 9500lbs. My truck has a class 4 hitch as well as an intergerated brake controller in the truck. I tow mine with no issue at all. I know the weight police are going to tell me I am wrong but I know what my numbers are and have been towing for years. I have scaled the truck and trailer and family in the truck and I come in just below my payload. Its not by much but we make it.
Good luck and happy camping.