You will be in for some experience, going from Perth to the snows of the Rocky Mountains..... in January!

Michael has given you the best advice available, but please note...

If the grand canyon is a priority, then I'd take I-40 out to it, and then work up to I-70 by going through Monument Valley and picking up I-70 near Moab.
I am sure Michael meant it the other way around. In his haste (he's very busy), he had you going from LA to Denver. So just change these instructions around. I can't help but agree, that if you have the time, that would be by far your best route.

Enjoy.

Lifey in Melbourne