I don't know the answer for you. It only costing twice as much is impressive, IIRC from previous searches for a trailer aluminum was about 3x.
If the cost comparison was $0.8K vs $1.6K, with my level of disposable income, I would pay the extra $800 for the lighter weight and theoretically higher resale value in the future. I suspect you are in a price range of $1.8K vs $3.6K, which would probably make me question whether I would do the same thing or just save the money for potential repairs to the truck. Additionally, for the purpose of driving a 4x4 vehicle to a once a month outing, I would take a heavier trailer with brakes on both axles versus a lighter trailer with brakes on one axle. I doubt the extra 800lbs of weight for the trailer will have a long term impact on the reliability of the truck, since they both fall under the max towing guidelines for the truck.
I would also look at Dodge forums to determine the anticipated lifespan of the transmission in that truck, especially when you start towing. I am very skittish with Chrysler transmissions based on seemingly magical ~100K mile transmission repairs needed that I have heard about from several friends with Chrysler products. I am assuming you have an automatic.