As mentioned, payload will be your biggest obstacle. Do you have fiberglass topper, added step bars, or any other accessory added to the truck since it left the factory?If so, they all add up toward your payload. Do you plan on taking firewood when allowed by the campground?
We had a 2010 Chevy Silverado 1500 CCSB 4x4, 5.3/6spd/3.42 w/ tow pkg- payload was a little less at 1554lbs, we were actually just over our GVWR (under awr's). It adds up very quickly! We do carry a few more things than some, ez up, coleman roadtrip grill, decent size tarp to make a nice shelter also when needed for cooking/ eating, etc. We hardly ever spend time inside the trailer unless we are sleeping or oven cooking. Camp chairs, have the kids beach toys during summer trips, fold up wagon for the beach trips, etc..Bikes for our twin 10 yr old boys, sometimes bikes for my wife & I as well. We also take firewood when allowed, aprox 300lbs or so.
Last trailer weighed about 6300lbs/860tw, the one time I weighed it. I moved some stuff around to slightly lower the tw, but never reweighed. Our new trailer weighs about 7200/920tw.
I never felt the need for more power (though it would have been sweet!) traveling here in Mi, just drop her a gear or two, and give her gas! MPG towing both trailers was anywhere from 7.5-10!!!
Just watch what you load in the truck, more so as the kids grow, and you should be ok for a while! It was this reason we just upgraded to a 2500HD-payload 2758lbs! Now the firewood and coolers can ride in the bed of the truck!
Good luck!
Chris