Either truck will handle that trailer weight with ease. The 2500 will allow you to haul more stuff than the 1500 will, but its camping... do we really need all the stuff that we bring??? I think that you will be able to keep the payload down if you try and it will work fine for you. I too bring the wife, 10 month old daugher, 3 small dogs and other assorted stuff when we camp. If you pack right and are aware of your payload limits you will be fine.
People talk all the time about how 1/2 ton trucks don't haul as well as heavier duty trucks. I have a Tundra 5.7 and tow a 6500 lbs travel trailer with no problems. My father in law has a 2 year old Chevy 2500 with the 6.0 gas and tows a lighter trailer (4 feet longer though). Both his truck and mine tow fine, his doesn't feel any more "stable" or "powerful" than mine. I get better mileage towing and empty than he does... but he has a much bigger gas tank than I do.
If the 2500 was in decent shape, I would certainly get it for the same price. Nothing at all wrong with a half ton, but I wouldn't turn my nose up at double the payload for the same price!
For the weight of the trailer, a half ton is perfectly fine for the job. With intelligent packing and weight distribution, the payload should be sufficient for a young couple with a young child and small dogs. When kiddo gets older and brings friends and bikes and other gear, you might want to research a heavier duty truck... but you have a couple years before you cross that bridge!
