I tow travel trailers commercially with my 2001 Dodge Ram 2500 diesel, now with about 458k miles. It was doing OK in the first year of towing, but after I hit 420k, it's been requiring major maintenance every month. Now it's in the shop for a rear axle rebuild, to include a ring and pinion change. My average trailer size and weight is 27 feet and 7000 pounds. I tow about 1200 miles a week, including long runs out west, but for the last few weeks I've been running through upstate NY and New England.
You are loading up pretty close to the Dakota's rated towing capacity, so treat the load with respect. I assume the 5-speed is a manual, so you should read the terrain and anticipate hills by downshifting to 4th for climbs and descents. You should be able to tow on the flat in 5th gear, but read your manual. If you are going to be using your brakes for hill descents, it would be a good idea to bleed them to get fresh fluid in the calipers. Since your truck only has 61k miles, nothing should be seriously worn out to pose a safety hazard in a 220 mile round-trip tow.
Never used 5th, not even on flat ground. Heard too many horror stories about shattering the overdrive gear to bother with it.
What do you do commercially, deliver travel trailers between dealerships? Even with repairs that kind of mileage is incredible.
Also, brake fluid is fresh as of 100 miles ago.