We did a similar trip in 2009. We drove trough Yosemite to Mammoth Lakes, then to Lone Pine and from there trough Death Valley to Las Vegas. From Las Vegas we made a loop trough Valley of Fire, Zion, Page, Grand Canyon and back to Vegas. The loop we did in 4 days.
I agree with Southwest Dave, it's a pretty long trip from Vegas tot Grand Canyon and do a tour on one day.
It's a beautiful trip so I wish you a great vacation!