I personally wouldn't do it because I've towed with a half ton before, granted by 2013, half tons were more Stout than the 2000s. And having your family ride in a different vehicle isn't going to change things. I'll explain.
My 3/4 ton is 7,700 pounds with everything in it, 9,200 GVW. With 2000 pounds of rock in the bed, it squats pretty good, I do that to drive a few miles home, no way would I want to do that on the freeway. When we all get out of the pickup, it doesn't change the squat in the rear even tho we are now at the 9,200 pounds. It's the same on your trailer, you are putting a strain on the very rear of the pickup way behind the rear wheels. You can try it, but I have a feeling you'll be disappointed in how it drives. The engine and tranny will perform great, plenty of power. But you'll feel every bump and dip in the road. If you are just doing a few miles down the road, who cares, it'll be fine. But any trip if any distance, you'll be left tired at the end of the trip. Whereas if you just got a 3/4 ton, you set it and forget it. The excess capacity is so worth it. I have never been "you forget it's back there", I don't get it when people say that. But the ride is so much more comfortable in a rig that's built for the job.
That being said, everyone is different and your pickup is technically capable.