You will definitely be going over a couple of good passes (10,000 ft, sections with 6-8% grades) going that route. You'll also see some of the most awesome scenery in Colorado. With a V8 Suburban, I wouldn't think you'd have any trouble, just take it nice and slow (well, you won't be able to do much else going up, will you??). Hwy 50, running from Montrose to Pueblo, is also very scenic, running along the Arkansas River, but it is a bit windy.
Take it easy, make sure you have good brakes, and you should have no problem.
p.s. "thedoors"??? As in the 60s-60s band with Jim Morrison?? My absolute favorite band when I was in high school....still is a favorite.