just for reference, my truck is rated for 6900lbs, with the included factory tow package that includes upgraded cooling, stiffer rear springs, better gear in the axle.
The trailer dry is something like 5100 lbs. I use a weight distributing hitch, air bags on the axle, and dual-axle electric brakes.
Throw in propane, 1/2 tank of water, firewood, pots, pans, bedding, tools, utility bits, and it adds up fast. My trailer loaded is probably closer to 5800, add it firewood and gear in the bed of the truck and we're easily past 6100 estimated.
Stock, it gets around town ok. On the highway for 4 hours, and it is stressful. It's all the truck can really do. The driveline is fine--- it has to spin up on the hills and I don't get in a hurry, but the stability is just not as sure-footed. air bags help a LOT, getting the brakes right helps a lot, but the truck just needs to be a little heavier to anchor that bad boy back there.
For the weights the OP is looking at, 1/2 ton towing to me would be occasional in-town only. Otherwise, bigger truck or smaller trailer.
For a family his size--- a 30-33' is a lot of camper--- we love the 24' we have-- the master bed slides out to the rear so we get another 6' of space once parked. Its perfect for 2, and works with 4 nicely as long as the time is spent outdoors. We are a family of 6-- and it works only as a bunkhouse and kitchen when we all go.
