I did some research last time to Grand Canyon, and found that Vegas just have too much stuff to do, the quickest is to take a air-tour from Boulder City. There will be shuttle bus from LV to Boulder City and you take the air flight from there.
That will cut down the trip time to about 5-8 hours :-) Tripadvisor is a good place to look for tour company reviews.
Also, driving to Grand Canyon is very un-interesting, not to mention there are parts of the Canyon are not car accessible.
Check with your autoplan agent, as you might have LDW or CDW coverage on rental vehicles. You just need to present the proof of coverage to the rental clerk, sign the waiver and that's it.