[Coley]

I've been through this myself....ie: 1/2 ton with an 8' camper.
First, you are going to need at least a load range 'C' (LT) tire, 6 ply minimum. (most are 235-75R15" LT Tires)
The load capacity and the plys should be listed on the tire....NO 15" 'P' (car) tires!!!!
I'm not sure if there is a (preferred) load range 'D' in a 15" tire....but look for one. There might be one in a Goodyear wrangler or a Goodrich to my memory....but don't quote me or my recollection.
Barring those choices you have a few different options.
If I was to do it again I would look for a set of 16"-6 bolt rims and get the larger (load range D) tires on those rims.
If not that you can look at using a 31-10.5" tire...goes on a 15" Rim but it is a little taller and a little higher than average rating compared to most 15" LT tires (ie: 235-75R15)
Anywhooo...with the bigger higher load range tires you get a very stable ride, good ground clearance, etc.
Good Luck, my two bits.
Coley
Question: What size is the camper? 8'? 8-1/2? Is it the one in the pic? It looks like an 8-1/2'er on a 3/4 ton. Be careful...its weight is probably very close to 1500lbs or better....I know this. Mine was an 8'ft and it weighed around 1300lbs dry....add another 250-350 lbs loaded or something like that. (ie: water/propane/supplies/etc). In my opinion the max lgth camper for a 1/2 ton is an 8'ft-er.