I have been running Far Away Land for her and her younger sister for a while now. I have detailed the first session of that game elsewhere. Far Away Land is an excellent RPG for younger players and we have tried most of the usual suspects. The core mechanic has very little math, it is flexible and vibrant and it also satisfies all my criteria as an experienced RPGer too. The setting creation mini-games are also fabulous for involving younger players and harnessing their ideas.
My daughter surprised me when she said she wanted to GM too. I think she was enamoured by having secret stuff behind a GM screen, but she has a genuine gift for storytelling and entertaining, so I agreed. Fortunately, Far Away Land has just started releasing a monthly series of short adventures. I would normally be reluctant to have used a prewritten adventure but the FAL series seemed perfect. I had run the first, Isle of the Rat Wizard, for the two and it had been a fun and simple affair. The adventures are 5-6 pages long and come with a cool piece of art and an even cooler map. So far, the adventures have consisted of a mini sandbox, with a settlement under a threat. They then detail various historical events, items, plot hooks, people, weather and monsters associated with that. My daughter also has a fascination with vampires, so the second in the series, "Whoa! Here Come the Dead", really caught her interest.
Though she is a good reader for her age, I sat down with her for half an hour and read it to her. We used a highlighter for the salient bits. We then had a refresher half an hour session the day before the game. She told me of things she wanted to add and I discussed how to do this, along with a series of other ideas she may want to use (assuming she would forget all of it).
When we got around to playing, I helped her along especially around rules calls and the like. However, she ran most of it by herself and she was amazing. In the climax, which she has added stuff too, she had a tendency for the self-indulgent (what GM doesn't!), ingrained on her from playing with her young friends, but overall she was conscientious and even ad-libbed ideas that blew me away. She also retained a lot of what we had discussed and never showed any sign of indecision or faltering during the 75 minute game.
The result is that she wants to run again and is eagerly awaiting November's "Crazy Maze Daze" adventure. My 5 year old has also demanded to GM, though I may work on a scene for her to do, given her young age :)
If you have young RPGers in the family, I can't recommend Far Away Land enough. Hell, its great for mature players too. Those that want to run with young players, I recommend using this character sheet that I created that allows for skills to be done freeform, and as pictures rather than words.