I had a couple of 1/2 ton trucks some years back towing 5th wheel trailers and........jee wiz they did the job just fine.
Running some numbers on your 1500 truck with a 3900 RAWR shows many of these size trucks can have approx 2500 lb rear axle weight which leaves approx 1400 lbs for a payload. Only you will know how much weight you add to the truck and if that weight goes over the trucks rear or between the axles. Not all occupants sit over the trucks rear axle which carries all the trailer hitch weight.
You have the truck so a trip to the scales for front and rear axle loads will be required so you will know what type of mods are needed to carry the load.
You mention 2400 lbs of load capacity for your tires which sounds like a P tire. If thats the case according to fed regs P tires used on a truck or trailer will have its 2400 lb load capacity reduced by dividing 1.1 = 2182 lbs of capacity.
Regardless for that size 5th wheel trailer I would go with a LT C (6 ply rated) or a D (8 ply rated) for your truck. Some folks go with a E tire however most 1/2 ton truck wheels aren't rated that high.
The Hemi with a 3.92/4.10 gears will have no problems pulling that much weight. Now if the truck has 3.23/3.08 gears then its gonna' struggle.
Check out these 1/2 ton size 5th wheel trailers
clicky link