The trailer you list is probably going to exceed your 3100 pound limit, and with the small V-8 and 3.55 gears you probably aren't going to like the performance. The only way to find out is to try it and find a good hill for a test.
A factory towing package is more than just wiring and a hitch. You will generally get things like a larger radiator, trans cooler, lower gears, heavier alternator, and whatever else the particular manufacturer deems necessary for towing. Also keep in mind that manufacturers' tow ratings are usually pretty optimistic. Things can get pretty frustrating when you tow at or near the limit.
curmudgeon: noun; a crusty, ill-tempered, irascible, cantankerous old person . . . .
79 27' Holiday Rambler Statesman, 78 32' HR Imperial, 85 36' HR Imperial 5th Wheel