Well, the first time I drove it was in 1963 in a 1953 Chevy with my wife and mother. The next time was in the late 70s with a '74 Ford pickup with a camper mounted on it. It is a beautiful drive! I would love to do it again but at 71 years old and a 30' motorhome I doubt that I will. I would do it in our '99 Jeep Grand Cherokee we tow if I had the chance. We drove that up Pikes Peak in 2014. It will be a challenge with your trailer but it is something I would have done in my younger days!
Best wishes, good luck, and enjoy if you choose to do it.
P.S. If your truck is in good shape, I wouldn't worry about its age. Our '99 Jeep has been in the garage for repairs 2 times at 103000 miles and I would drive it anywhere that I would drive my 2014 Chevy pickup that has 18000 miles!:W :B