As previously stated the answer is Maybe. There is a lot more than overall manufacturers stated tow capacity to look at as that number is given on a best case scenario with nothing but a driver in the truck..... let's look at how to figure out what you can tow.
First load your truck up with all passengers, pets and gear that will be with you when camping. Now go to a local Cat scale
and weigh your truck with a full tank of fuel plus all of the above mentioned items. Put the front axle on the first scale pad and the rear axle on the second scale pad. (Bring a broom handle as the button to push us at truckers height).
Now take your trucks total scaled weight and subtract it from your trucks gcwr (gross combined weight rating) to get your adjusted towing capacity. Take your trucks scaled weight and subtract it from your trucks gvwr (gross vehicle weight rating) to get your available payload. Take your rear axle weight (drive axle on the paper) and subtract it from the max rawr (rear axle weight rating) to find out how much room you have available on your rear axle. You need to stay within all of these numbers with your loaded tt weights.
Your trailer tongue weight will be applied to your truck's payload. The dry tongue weight listed is kind of a useless number as it commonly does not include propane, battery etc. Your ideal tongue weight is 13-15% of the trailers loaded (not dry weight). You will not be taking a empty or dry trailer camping. Since you don't know how much weight you will be putting in, it is safer to calculate using tt gvwr, although I will tell you that on average people tend to add 1000-1500 lbs of gear, dishes, clothes etc to their tt.
Once you look at all of these numbers you will have a pretty good idea of what you can tow. Don't let a salesman talk you into towing any heavier than that. Happy hunting.