I have the same year truck you are thinking about except it is a SRW. My 5th wheel weighs 12600lbs loaded and my truck pulls it fine with a 3.73 axle. And I also pull doubles with a 2800lb boat/trailer behind at times. Still does well, and I do much of this in Colorado! Big hills to pull.
You should be okay with what you are considering, IMO. As far as limited slip, if you get a truck that has it fine, if not you still will be okay. Mine has it but I cannot think of a situation I have been in that needed it while towing. In the winter when just driving the truck it has been handy.
