Difficult question.
Personally I'd look beyond the question of language and instead focus myself on "how could I teach her to program?", or the basics of programming.
Sure, she'll be looking for quick results; but you could use that to some advantage by providing her with some tools which can have much longer lasting results. Heck, she might even discover a field within IT which she actually could enjoy.
And with that in mind I'd personally focus a bit on Java since it's relatively easy, can be used on several platforms (and to some extend even mobile platforms), the developer tools (such as my personal favourite
NetBeans) can be used free of charge, and it's still pretty widely used (not too arcane or limited so to speak).
Most of all it should be able to provide a quick solution to a problem.
Still, whatever you do I'd strongly suggest not to try and steer things too forcefully. If you start trying to actually push her into a direction which you think is best then you seriously risk putting her off and she might lose interest in this field altogether.
SO even despite what everyone (including me) says do make sure that whatever you decide to suggest also fits her interests.
For example; if she's also looking forward to building stuff which her friends can also use (and let's assume they all use Windows) then Java might not be the best pick due to the requirement of an JRE. In that case I'd focus more on C# (or maybe even VB) because both will operate within the .NET framework.
Alas, my 2 cents on the matter.