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Depends on how motivated she is to learn (or how good of a teacher you are). If you expose too much complexity in the very beginning, you may risk her not liking it from an early age.

I can come up with one idea which would have been super fun for me as a kid (game AI with python, look at Berkeley CS188). But I would have needed a lot of direction. And maybe that idea is overrrkilll.

There are also some flash games which let you do things like programming. But it may not be fun and it exposes no complexity.

There's also this sort of thing: http://en.wikipedia.org/wiki/Scratch_(programming_language)

I have no experience with it and I can't say whether a kid would find it fun.