Julius- Can't emphasize enough to remember that to focus on her enjoyment will make or break your walk. I've seen an 18month,3 yr old ejoying the R2R with their dad, and mom and the teenage daughter were ready to just get it over with; largely due to the additional weight they were carrying to compensate for the little ones and dad having a child carrier.

Stop at the bookstore and get the Trailguides for the N.KAIBAB and the Bright Angel. There are a lot of interesting history, geological and wildlife info; so you all can appreciate whats being walked through. There are other books for kids that may be of help to keep her interest.

Phantom Ranch lemonade is a must.

Don't rush, help her focus on the neat things you'll see; keep her eating and drinking fluids regularily to keep her energy level up; take breaks; and remember her body hasn't developed nor does she have the experience to let her (and you) know what is going on her body. Kids tend to go until they drop-they haven't learned how to pace themselves. Pay attention to her, and when you see/hear something that is different than her normal personality- stop and fix it.
Families have a great time when they focus on enjoying the experience; and not being focused on a 'timeline' based on adults priorities.
These tips are for any activity- Whitney included. The big difference is that at Grand Canyon one starts at the summit, walks down to base camp; then walks back to the summit- The reverse of most other hikes; and explains the looks you'll see of hikers going back up on both rims.