You don't go thru Vegas from the Grand Canyon to Anaheim. If you were going to Vegas, you get off I-40 at Kingman and take a different highway to Vegas (going over Hoover Dam). Going to Anaheim, you stay on I-40 to Barstow, then go south on I-15 to Anaheim. It is just a bit under 500 miles and with traffic going south to LA, it could take 10 hours. Its all going to depend what day of the week you are driving and time of year. Your timing should be better during the week vs. a Sunday and hopefully no major accidents to slow you down.
I grew up in SoCal, lived/worked at the Grand Canyon for 18 months and have a sister in Vegas so I've made every combination of this drive over the years.
Its a long boring drive for me but if you've never been out west and through the desert, the scenery will be like nothing you've ever seen.