IMO the truck won't have any issues in the mountains. Sure you won't keep up with the V10 Fords or the new gen diesels but just take it easy and enjoy the trip.
I pulled a 8600 lb trailer all over the southern Rockies with a '90 chevy 5.7 with 215 hp and 300 ft lbs of torque 4L60 and 4.10 gears.
Your 5.4 has much more power and a lighter trailer. Going to 4.10 gears would help with acceleration and pulling duties as with any smallblock combo. Make the trip first and then decide if any expensive mods are needed.
I did add a cat back big block Flowmaster and a K&N too help the engine run cooler and a big aux tranny cooler. Ran the truck for 232k miles.