Looks like you have the following factory towing options:
KNP - NG SYSTEM TRANS, HD 913 (Trans Cooler)
VR4 - TRAILER HITCH WEIGHT DISTRIBUTING PLATFORM
Z82 - TRAILER PROVISIONS SPECIAL EQUIPMENT, H.D.
Like me you also have Hydro Boost Brakes which will help greatly with a trailer:
JH2 - BRAKE HYD POWER, DISC/DISC
The main difference from my setup is that you have the following:
GU5 - AXLE REAR 3.23 RATIO
M30 - TRANSMISSION AUTO 4 SPD, HMD, 4L60-E, ELECTRONIC
I have a 3.73 rear and a HD 4L65E transmission.
Take a look at the "Tech Specs" tab here:
http://chevroletforum.com/forum/vindecoder.php?vin=1gnec13z36j116588
And Page 23 here:
http://rvbonus.com/towing/2006/2006tow.pdf
You have a 5,000lb tow limit with the hitch as-is, and a 6,700lb tow limit (2WD) with weight distribution. I know lots of people tow right up to the limit, and some beyond, but I like the rule of thumb that your default setup shouldn't be much beyond 80% of your rated max for comfort and stability. For you that would work out to 5,360lbs.
With the camper you are looking at with a dry weight of 4,295lbs that would leave you around 1,065lbs capacity for cargo.
On paper it seems tow-able, but if you are going to do a lot of long distance towing you may want to swap out your rear to a 3.73 or 4.10. You can see on Page 23 of that towing guide if you upgrade to a 3.73 with your 5.3L 2WD the tow rating increases to 7,700lbs with a weight distributing hitch.
Also, if you ever needed to rebuild your trans, a 4L60E can get rebuilt as a 4L65E with the upgraded HD components.
Additionally, if your front brakes are coming up for service you could also benefit from the NNBS front brake retrofit and take advantage of the increased bolt on braking capabilities.