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I was thinking of something like http://www.squeak.org/ or http://scratch.mit.edu/
What do you think?
One way to sort of ease into the idea of instructing-a-computer-so-it-does-things is to make things in a context-free-grammar based system, like: http://www.contextfreeart.org/
I've found some people find it much easier than "real" programming, since it avoids control constructs and such. I personally actually find it a little harder, because I try to think of it in terms of operational semantics, and end up mentally reverse-engineering everything I write into the equivalent C code. I've had good luck introducing non-programming people to it, though; not tried with any kids; mostly computing-interested adults.
Processing is a relatively simple media-computing environment. Based on Java, but highly simplified and oriented towards 2d graphical applets: http://processing.org/
I personally learned on Logo, which I thought was nice. I'm not sure if there are good Logo implementations these days?
http://www.microsoft.com/downloads/details.aspx?FamilyID=B00...
A good overview can be found here http://msdn.microsoft.com/en-us/beginner/ff384126.aspx
PHP is mainstream, and since it's a web technology, she can likely show it off to her friends. It's not hard to find cheap PHP hosting if she ends up building something that she wants to put on the public-facing Internet for friends or strangers to use. XAMPP also comes with MySQL pre-configured, which is a bonus.
I cut my teeth on Logo and BASIC as a youngster. I wouldn't wish BASIC on anyone, and she's old enough that Logo would be boring.
Having said that I'd probably get her a HTML/CSS book.