For the starters, the sticker weight rating is done for tax purpose and has not much to do with real truck capability.
I was carrying 4500 lb of gravel on F250 just fine, but with camper the next issue is going to be weight distribution.
I bought my 4200lb camper with F250 and stop at the scales both ways.
Turn out that due the center of gravity the camper put close to 5000lb on my rear axle.
I had to buy dually to use the camper.
From numbers you have, your truck should carry the weight just fine, but start with checking your rear tire ratings, than analyze the camper center of gravity.
If you have rear tanks, that could create issues.
This way, or the other air helper bags will be strongly recommended.