If the camper is designed for a LB then generally it will need to be FULLY supported by the long bed. A camper's floor might not be designed for that cantilevered portion sticking back... and don't rely on a folded-down tailgate as they are not designed to support weight and could even damage it.
I say "generally" because there are some models that are designed to be able to go on either a long or short.
Even if it can work, is your truck set up to carry a camper? It looks as if you have a Ddge Mega cab... do you have tie-downs, 7-way plug?
edited for speeling koreckshun as noted in red.