Wondering if I could safely tow this travel trailer?

The biggest issue is probably the rear axle ratio. You will likely need some thing like a 3.7 or higher.

The 3.42 paired with the new 6 speed tranny pulls like a 3.9x-4.1x axle ratio depending on gear slesctions.
The only option is a 3.73 (NHT package) paired with the 6/8 speed. We drove one before the wife choose her truck. The 3.73 remined me of the old 4.56 gears in the older trucks.