Controlling the load is the most important thing. Your truck can control that trailer. You need a frame mounted hitch and a trailer brake controller--an inertial type, like a Prodigy, not a time-delay type.
The rating on your truck is partly to sell you the more expensive package--4.0 and auto. Secondary to that is the fact that an auto is easier to drive while towing and less likely to cause a warranty claim.
An asshole might slip the clutch mercilessly trying to get the trailer to take off faster than it wants to. It might kill the clutch in one day.
Get the clutch fully up as smoothly and quickly as you can and then apply acceleration. Don't push the gas pedal down more than it takes to avoid stalling until your clutch foot is off the pedal. After that, don't use the clutch. I mean, use it, but don't. Rev to about 4,500rpm in each gear, let the clutch all the way back up before applying gas. You'll find the place where you can do this smoothly. You can tow 6,000# and your clutch will die of deterioration before you burn it. The simultaneous clutch out/gas in thing is what kills clutches.
My 4,500rpm thing is a guess. I've never driven a 3.0. Point is, you are asking for a lot of power and you need to let the engine make it. If the max power is at 5,000, shift there when you are towing. That will keep the engine in its torque band. If the engine is allowed to make the torque, it takes the load off of the drivetrain.
