Skip to the stars for summary

I just recently bought the Call of Cthulhu core book from Chaosium, and in preparation for the upcoming game I'm going to run, this book goes everywhere with me. Every spare second I have, I crack it open and review Mythos, rules, or stats, just to make sure I've really got as solid of a grasp as I think I do.
So, it came with me while I was out visiting my mother. There's some down time, so I'm sitting on the couch reading about sanity loss, and my little sister come up to me, points at the book, and says, "Jacob, what's that?"
I paused for a minute, thinking about how to explain it. I said, "Well, it's a game, but not like Zelda or Mario. You play it with other people, imagining what you're doing instead of seeing it on the tv. It's a lot more complex, too. In a roleplaying game, you can do
anything you want to, from killing a dragon, to building a chair. As long as it fits the game world, you can do it."
She asked me what CoC was like in particular, to which I tried to explain about evil gods and ordinary people caught in extraordinary situations. I also told her that Shadowrun was set in the future, with magic and robot body parts, and that D&D was fantasy, with knights and wizards, and trolls and dragons.
To which she replied, "Oh. Okay."
Well, hey, whatever. Maybe she'll ask again in a few years.
Next day, though, as I'm getting ready to leave, and am heading out the door, she says " Jacob, I'd really like to play Shadowrun, or D&D." (Remembered the frakking names. She
was paying attention

)
So now I'm stuck with a dilemma. I can not pass this up.This is going to happen, no matter what. BUT, I don't know what the hell I should have her play. I've rolled it around in my head, and I've come up with a few conclusions:
1.
NOT Call of Cthulhu. Not an investigator's chance in R'lyeh. Not only is the explanation of the Mythos way too much to make her sit down and listen to, it's just not something that really jives with a ten year old. "What? I just got eaten? I HATE THIS GAME!" So on and so forth.
2. I'm iffy about Shadowrun. She doesn't really have any prior experience with cyberpunk, and sitting her down to watch the dull as a butter knife snooze-fest Blade Runner (I like Blade Runner, I really do.), or lending her my copy of Neuromancer as a reading assignment doesn't seem like a good idea.
3. D&D; Fantasy = Good. She's got more experience with a fantasy setting than the other two. She loves Lord of the Rings, Harry Potter, and the aforementioned Zelda series. She's read the Percy Jackson book and loved them. Likes Egyptian culture and all their "funny" gods. Lot of background there. But D20 isn't my favorite system, nor do I feel that it's the easiest to learn. Especially preparing spells. I've read the section twice and am still hazy on why the hell they did it the way they did. I also don't really feel the little nasty surprises, like attacks of opportunity, will be too popular, especially since I've found they almost never end up working in the player's favor.
********************************************
So, what systems, settings, genres, or styles of play do you feel would be best for introducing a young girl to the world of role playing games? What ways would you change any of the existing systems to make them more accessible to a younger audience?
Then again, maybe this is a case of, "Yeah, but your scientists were so preoccupied with whether they could that they didn't stop to think if they should."
Thanks in advance!