You will almost certainly need a DRW truck. You really need to look more closely at the camper specs. On the webpage, this camper starts at 3340# dry weight. Wet weight will be very close to 4000# without options. The list of options is really long and includes many must have items. You need a more exact weight for the specific camper configurations. Then figure close to another 1000# to outfit the camper with food, clothing, tools, emergency air compressor, kitchen gear, bedding, generator, fuel, lawn chairs, BBQ, cleaning supplies, etc, etc. I can almost guarantee you will hit at least 500# if you are careful on keeping the weight down. Don't forget to add additional weight for passengers, truck modifications such as a bed mat, brackets and tiedowns. It is very likely that you will hit a grand total of 6000#.
You will almost certainly also want to use a diesel to pull this rig.