2800 lbs dry camper of that size will be 3600 lbs by the time you include factory/dealer options, battery, propane, and your own gear. Assuming your tow rating is calculated like most trucks, that leaves you with only 400 lbs of capacity for any passengers and truck cargo (beyond the driver).
If my 800 lbs estimate (over dry weight) is accurate, I think this is too much for you. However, if you can get a look at the 16BHS interior, there should be a sticker showing the ACTUAL empty weight, including factory options. As the dealer to estimate the weight of their options, or even better if they can weight the actual weight for you. Then you can estimate the weight of your own gear.
All said and done, you need to be sure that the total weight of the loaded camper and all passenger/cargo in the truck, do not exceed 4000 lbs. This might limit you to a high-wall popup camper. And for a 5-cylinder motor, that's probably best anyway. You would have trouble pulling a full-height camper of any weight on the expressway.
thebrakeman ('70), DW ('71), DD ('99), DD ('01), DD ('05)
2004 Surveyor SV261T (UltraLite Bunkhouse Hybrid)
2006 Mercury Mountaineer V8 AWD Premier
Equal-i-zer WDH (10k), Prodigy Brake Controller