It will fit with almost no problem but will be a bit tighter than on the older truck. I'm carrying a 2004 Lance 815 on a 2015 Ram. They are both the same dimensions as the 2003 and 2016 you are planning on matching.
The only thing I found was the bed rails were a tad high on the new truck. The plastic bed rail caps just touched the camper at the very back. While it wasn't putting any real weight on the bed rail, it was enough that if you put a piece of paper on it before loading the camper, you couldn't pull it out. So I made a 3/4" platform (1x6 perimeter with 3/4" foam interior) but a 3/4" horse stall mat would have worked just as well. Load it up first and you may decide you don't even need anything.