First, I am no "expert". Is that 1135 number the Payload number on the yellow door sticker? If so, the trailer you mentioned is probably over your max. That 1135 will be reduced by the weight of passengers and other "stuff" you may be hauling, like extra fuel, generator, tonneau cover, hitch, etc. It could easily get down to 600 pounds. Add to that the fact the tongue weight can easily be well over the published 600 pounds, and you can see the problem. Personally, with your truck, I would be looking at trailers with dry weights under 5,000. One "Expert" tip is to get actual weights before spending any money.
