What is the make - model of your 3500, is it diesel or gas, and is it a dually. Does it have the "tow mode" feature and cruise control
I have a 3500 Chevy Dually long bed crew cab diesel truck. It has all the above mentioned feature and I tow a 41 foot fifth wheel, and the trailer weighs in around 14,000 pounds. We travel from Central Indiana to the mountains of North Carolina, from Central Indiana to Louisiana, and from Indiana to South Dakota, and sometimes a circuit hitting all 4 destinations in a single trip. We cross mountains, prairies, hills, flatlands, snow, ice, tornadoes, escaped hurricanes, blazing heat, and blizzards towing our current camper. We've never traveled anywhere, under any conditions that our truck did not perform well.
I use "tow mode" and "cruise control" and let the truck tow itself. Travel no faster than 60 mph to maximize the best fuel mileage, and have never experienced a "white knuckle" experience (except once when the trailer brakes went out).
Let us know what type of truck you have, but you probably have more than sufficient with the 3500. There are maps available on-line that let you plan trips based on the flattest elevation.
Good luck, enjoy, and happy camping.