OK, here is the raw data (with source links) and you can draw your own conclusions:
Truck Specs: 2007 GMC/Chevy 1500 STD Bed Ext Cab w/ 5.3 engine and 3.73 gears Factory Tow Package:
2007 GMC Sierra 1500 2WD Ext Cab 143.5" SLE2 Specifications-Vehix
Max Combined weight - 12,000
Max gross weight - 6,800
CURB weight Front Axle - 2,824
CURB weight Rear Axle - 1,965
Total Curb Weight with SLE2 package - 4,789
MAX axle weight rating Front Axle - 3,600
MAX axle weight rating Rear Axle - 3,750
Max Tow Rating - 7,700
Maximum payload - 2011 (GVWR minus Curb weight)
The Camper's Specs are:
Flagstaff 2009 8524RLS
Length - 26 feet
DRY wt - 5,823
Dry Axle wt - 4767
Dry Hitch wt - 1056
Dry axle to hitch ratio - 18%
Maximum Payload DRY - 1,900
Maximum Camper Gross weight - 7,773
Optimized Pin Weight Load at Max gross weight
15% MINIMUM for safe handling - 1,166
18% DRY Ratio at max gross wt - 1,400
20% Optimum Pin Weight - 1,555
25% MAXIMUM SAFE pin wt - 1,943
Now to go any further we need the Unloaded Vehicle Weight (UVW) off your yellow sticker on the side of your camper (or inside one of the cabinets) But for now, we will just use the DRY weight AS IF it was the actual UVW. The UVW could actually be several hundred pounds more than the listed DRY weight due to factory installed options; like air conditioning, Ladder, spare tire and holder, batteries, propane tanks and full propane, etc)
So, To find out what is left over for pin weight you must weigh the truck unhitched as you would travel for camping. All the family with the dog; a full tank of gas and the hitch installed. Any junk you normally carry in the bed should also be aboard.
Subtract that actual weight from 6800 pounds to find out how much your pin can weigh; then load accordingly.
You must also take care that your combined weight does not exceed the MCWR of your truck.
For example, if you max out the truck at 6800 pounds; the camper can't weigh more than 5200 pounds (12,000 - 6800) oops
If you max out the camper your truck can't weigh more than 4,227 (12,000 - 7773) also oops
Using the DRY weight (must use UVW here when you get it); say you only use about 1000 pounds of your stuff in the camper. Food, DVDs, cool mods, and water for flushing. That will make the camper weigh 6,823 pounds (say).
At the optimum balanced load for safe handling (20% pin weight) you will carry 1365 pounds of your camper's weight in the bed of the truck.
12,000 - 6823 = 5,177 pounds left for the truck to weigh.
That means your wife; dog; kids; spare gas can; and hitch can't weigh more than 388 pounds combined. Since a 5th wheel hitch can weight between 75 and 200 pounds, things get interesting very quickly.
I hope this helped with your question and gave you some tools to play with the numbers. To answer your question: Can a "half ton" tow a "half ton towable camper" the answer is "absolutely." You might just have to have the family follow you in the car, though.