My 2010 F150 truck does a great job towing my heavy 4200 LB OFF-ROAD Starcraft 14RT OFF-ROAD POPUP Camper.
I certainly would give it try without one... If it pulls your truck down towards the ground big time then definately get one. My 2010 Truck tow package has some sort of sway control built into it.
Since 2008 I have a good 50K-60K tow miles on my off-road camper... Even around wiskey Tall Falls and Wichita Mtns Wildlife Refuge in Medicine park OKLA. Used to go to Midland/Odesa on Tornado alerts way back in my running around days with Ham radio OPS out your way... Married into North texas and lived there in the 60's and 70's. Love looking straight out and seeing stars at night.
Roy Ken