Suggesting some programming language (say, Python, or Ruby!) is silly, don't teach her a programming language, teach her how to do something
Something you mentioned in the question is a great idea to expand on,
LSL scripting in Second Life
Improving a game you play is a great reason (and a great way) to learn programming.
Introducing someone to programming is entirely about getting the person to want to program - a video-game is a really visual, rewarding place to see your work. Seeing your name printed 100 times in a terminal is pretty boring compared to making stuff fly about and explode and such.
I first got first got interested in programming when I was young is because of Lego Mindstorms. To illustrate my point, compare if I started in Python, compared to Mindstorms:
Python:
import time
print "forward!"
time.sleep(1)
print "turn left!"
When I run it, in a terminal it would output..
forward!
turn left!
Lego Mindstorms:
Add-and-drop "output 1 forward" block
Add-and-drop "output 2 reverse" block
Add-and-drop "Wait 1 second" block
Add-and-drop "output 1 reverse" block
Add-and-drop "output 2 forward" block
When I run it, the little Lego car I built starts moving around, just like I told it to do!
After Mindstorms, I started learned about HTML by using Front Page and looking at the "Code view" while adding tables and stuff (so learning HTML while I made websites). I then started learning PHP because I meant I could add dynamic stuff to the web-page, like taking ?name=ben
and putting it in the HTML by adding `!
Around the same time, I started playing "Operation Flashpoint", making missions using it's mission-editor. You could add _this setdammage 0
in a area-triggers code-box to heal any unit that entered a certain location (say to have a functioning "medical tent").
While I'm not suggesting Lego Mindstorms, or PHP, or Operation Flashpoint (although Lego Mindstroms is great, it might be a bit "childish" for 15 year old), my point is: seeing cool results is more important than learning something "useful" (like a real programming language like many people seem to have suggested).
Don't even consider mentioning a language, or doing it professionally, or force her into learning it - just point out the cool things you can do! Find something she's interested in, and show her the "script editor" button.
Something that just sprang to mind - something stereotypically popular with teenagers - Myspace and the likes - they generally lets you change the layout of your profile with CSS. Show her how to take the output from one of those "custom myspace style generator sites" and change the colours about (by adjusting the background: #aabbcc
bits). It might "not be programming", but it's changing code and producing really visible results in the browser - somewhere most people don't even think about.
Actually, Lego Mindstorms didn't get me interested in programming - it was when I was in primary school, my teacher pointed out that someone had to program traffic lights so the lights turned on and off. It's something I never even thought about until then..
All you should really have to do is create the link in her head between "programming" and all these web-sites and video games she's interested in..
(Err, slightly long and rambling answer, which isn't so much entirely aimed at the original question, but rather many of the other answers, which seemed to be going about things the completely-wrong way)