That's towards the top end for a half-ton, but you should be fine.
I towed a 6000-lb trailer with my '01 Burb (5.3, 4.10, custom PCM tune), and the Burb has a lot more weight on its rear axle, which, for the Burb, is the limiting rating.
You're not going to win any races. We went over the continental divide in Wyoming (9600 ft elevation), and the best the truck could do was first gear and 25 MPH. Keep it around 60-65, and you'll be good.
If you are taking a long trip in the summer, invest in a handheld infrared thermometer to check your rear axle temperature. My Burb is on its third rear axle. Hence the upgrade to the 08 2500.