Towing with Pentastar V6 pickup truck

I question the 4500 rating. Might be "up to" and what that means is this:

Manufacturer builds to a Gross Vehicle Weight Rating or GVWR and a Gross COMBINED Vehicle Weight Rating or GCWR.

Let's say empty truck and empty trailer weigh 5000 each and GCWR is 10000. By specs you're good to go. My experience with rigs that are right at GCWR, is they're pretty doggy, get poor mileage and don't handle well. Now put 500 in the truck. Trailer can only be 4500. Put 500 in trailer and you're 1000 overloaded to the ratings.

Your geographic location reinforces my NO! You won't be happy with it. Flatlands, maybe. Tow it to the Lake and leave it set up for summer then tow it back home, OK. Actually Travel and Camp? Out there with two adults for two weeks and maybe more people or longer trip? Nope.

Obviously the towing platform is very up to the task. The drive train is where it gets a little hairy. I believe you will be perfectly safe if you've taken the standard precautions with maintenance, hitch setup, tire inflation, etc. But you really will be under powered, which will be most noticeable on hills. I bet it could be done just fine, but I wouldn't want to be the one doing it.

For long distance towing 50% of advertised tow capacity works nice with pickup trucks, especially gasohol engines.

When loaded for camping, that trailer will be closer to (if not over) 5000 lbs, with tongue weight in the area of 600 lbs.

Look at the tire / loading sticker (on drivers door post) for the truck, as it was leaving the factory. You'll find a number for "max occupant / cargo weight" (AKA payload). That is the truck's capacity to carry the combined weight of everybody and everything that gets added to the truck. That includes aftermarket accessories (undercoating, bed liners, bed caps or covers, etc) that you or the dealer have added.

Check your hitch receiver. It has it's own ratings for dead weight being carried and one for weight with a weight distributing hitch.

The weight of your hitch equipment and trailer tongue weight are counted as cargo weight in the truck. If you're using a weight distributing hitch, that weighs 80 - 100 lbs.

Your payload number should be high enough to support the weight of your family, pets, any cargo in truck bed, and up to 750 lb from hitch and trailer.

Youre not going to hurt the truck or be unsafe to tow at or above the 4500lb tow rating.
May need to take it slow up hill and you'll be towing in lower gears. The 8 speed ZF is a great trans. Even still, these newer V6s have similar or better power than many of the older small blocks still on the road.
Remwmber, same basic truck that is configured to tow over twice as much with minimal differences than more power, deeper gears and possibly larger trans cooler package. I'd look into that but that's an easy addition.
As long as you're good with giving the engine a workout.

If the only difference really is the rear end gear (the cooling and everything else stays the same), I have always felt that the transmission can be downshifted to get the RPMs back up where they need to be for good torque & HP output. But if your rear end gears are smaller and lighter weight than the 3.55 set, they could be damaged (Toyota Tacomas, for example, put a smaller diameter gearset in the rear end of a 4 cyl than what their V6 model gets).

That said, I think you will be pushing your drive train harder than you like to tow that trailer. In practice, your loaded weight will probably be more like 5500 lbs once you add LP, battery, water and gear to that dry weight. (And your hitch weight could easily exceed 700 lbs if you aren't careful how you load it.) I towed 3000-3500 lb (loaded weight) trailers all over the country with a 270 HP V6 in a Toyota, and I know I would not have wanted to try towing the unit you mention with that size V6.

The Pentastar was rated for 290 HP just a couple years ago; when they tweak for more HP, the torque usually doesn't increase correspondingly. It would struggle hard on any long or steep grades.

If tow rating is 4500 pounds, you'll want to target closer to 3500 pounds. For towing any high walled RV, make sure your vehicle has a heavy duty transmission cooler. Pulling two sheets of plywood through the air at 60mph takes a lot of power, which means the trans shifts a lot more than just the truck itself. The 8-spd trans will keep the engine in closer to it's peak torque, so expect a lot of time towing in the 3000-5000rpm range. IF that scares you, get a low walled RV or different vehicle.

Based on the information you've posted you'd easily be exceeding this truck's recommended towing capability as no one tows an empty trailer. It's the trailer's GVW loaded & ready to camp, along with it's average gross tongue weight, on which you should base your determinations.

Your truck is not really designed to tow much. Pulling 5,000 pounds is going to be hard on it.