If she just wants to make web pages, set her up with some webspace and then, after she's gotten HTML and CSS down, show her that she can "make things happen" using PHP and Javascript.
If she wants to make a game, I would personally recommend starting off not with any raw-coding environment at all. Why? Kids don't generally like designing game mechanics—and that's what they're tasked with if they have to turn a general-purpose programming environment—or even a multimedia environment like Flash—into a game engine. If they say they want to make a game, chances are what they want to do is just to re-use ideas they've seen in games they've already played, but with different content assets and "individual-asset mechanics" (i.e. new power-ups, weapons, etc.)
My own recommendation, then, is RPG Maker, partly because it's where I got my own start in logical systems-based thinking, but also because it has a nice, gradually-sloped learning curve, beginning with pure level design, and then transitioning into scripting as the need arises, before finally peaking with the limited ability to rewrite the game engine in the scripting language itself (with just enough chafing to make them crave a better tool.) The only catch is that it isn't free—RMXP is $60USD, as far as I'm aware.