These numbers are from the Keystone web page:
The RV has a 5030 shipping weight - this is dry weight - 1 battery and no propane in the tanks.
It has a 2510 lb carrying capacity
Potential weight - 7540 lbs.
The GVWR of the 1500 is 7200 lbs with the 5.3 L engine and 6900 lbs with the 4.3 L engine
That is too much trailer for a 1500 truck - go for a 2500HD Silverado and that will give you margin on the GVWR and may help in the future if you get a heavier RV.
Silverado 2500HD - 9500 lb GVWR with the gas engine and 10,000 lb GVWR with the diesel engine.