Are you driving to the Grand Canyon, or taking a bus/plane tour?

If driving, be prepared for an exceptionally long day. I'd leave early (from Vegas I'm assuming), as in 7am at latest.

Also keep in mind that the South Rim of the Grand Canyon is at about 7,000 feet in elevation. It is generally 20-30 degrees colder there than central Phoenix. If you go through Flagstaff, it may be even cooler (the low this morning was -1F).
Along with cool weather, be prepared for winter conditions. The ski resorts in Flagstaff opened on Thursday, and if there's any rain in Vegas, chances are there will be more snow at and on your way to the Grand Canyon.

The advice others gave is mostly spot-on for freeway driving, but it really depends which state's license plates are on your car. Since I live in AZ, while here in AZ I can usually go 10 above the speed limit without issue. But I've seen cars with Texas plates get pulled over.
For non-freeway driving, I'd exercise a bit of caution. You'll be in unfamiliar territory, the roads could be windy, and possibly hazardous. Some of the smaller roads in Northern AZ aren't in the best shape either (most highway money is spent here in the PHX area).

Have a great trip!