I looked at the Toyota Tacoma, but the specifications say 1120 lb maximum payload,
The 1120 lb number is a gvwr based payload which is spread over the trucks front and rear axles. However add 1120 lb in the bed may overload the rear axle/tires/suspension/wheels (RAWR).
I'll throw some payload number at you.
If your set on using a new model 1/2 ton truck to carry a truck camper then Fords F150HD has 4800 rawr which is good for around 2400-2500 lbs in the bed. That will include the fully loaded camper and all your "stuff" in the truck.
The new gen 3/4 ton trucks have 6000-6500 RAWR and are good for up to approx 3200 lb payload in the bed.
A one ton SRW may have around 3800 lbs payload in the bed.
And the one ton DRW with those big 9375-9800 RAWR can have around 6500 lb payload.
All numbers are approx numbers so payloads for any truck can be determined by actual scaled axle weights.
Or just use the truck makers GVWR based payload. Both are safe.