I just drove from Moab to just outside of flagstaff pulling 21 foot 5k fifth wheel with half ton Chevy with the 5.3L engine.
I highly recommend that you get a 3/4 ton. Going out of Moab I was pegged at 35-45mph in a one laner for about 10 miles, and going up towards flagstaff fortunately they have 2 lanes so I could just sit in the right lane and slowly drag my ass up the mountain going from 40-55 depending on incline. So, it can be done, but a 3/4 ton is going to be purchased as soon as possible.
It's no fun driving and constantly having to watch the gauges making sure it doesn't over heat and blow up. Occasionally you will have to pull over for 30-45 minutes and let it cool down, especially going over the passes when you get to the top.
Another thing to consider is the decent, it's not bad except the passes. I ride in 3rd or 2nd gear and still have to ride the brakes on the steep parts, with a bigger truck with a better tranny it'll just do the work for you and save the brakes.
If 1/2 is the only vehicle in the budget it can work, but it'll be a hassle anytime you do the mountain driving. If you do go with the half ton, a 5.7 liter should improve it quite a bit as well.