Make a simple program. No, not "Hello World!"

What'd I'd do is say that there are many types of programming languages -- ones that make games, ones that control robots -- but what you're going to be working with is HTML.

Make a web page with nothing on it, and then add an form that will send an email to her email address. She presumably has a cell phone that is capable of notifying the owner that they have a new email, so you could tell her that it's a great way for her friends and family to contact her. If she gets her own web site in the future, you can tell her that she can put the form on her web site, allowing her customers and business partners to contact her.

Alternatively, if she's a little mischievous, I'll tell you what got me interested in programing: hacking. Back in the day, I made the best program ever made for messing around on AOL (outside one program that outperformed mine in only one of the dozens of things that mine did) -- at the age of 14-15. On the white hat side, I also made one of the first spam-removal programs as well (1995.) I was able to make my online experience a lot more enjoyable, and we'll leave it at that. Everything that I wanted to do on a computer was an adventure or puzzle that I had to figure out, and the things that I wanted to do on a computer were endless. Sure, getting it to work was a headache at times, but writing a program that accomplished things better and faster than any human could, or doing things that were simply impossible to the general public, was like building a fine piece of machinery that one could be proud of. Now, you probably out to shy away from anything serious, but it would be extremely easy to make something in Visual Basic that could be launched on start-up (sitting on the side of the screen or the system tray,) and from there, you could make it launch her favorite web sites, her favorite programs, etc. You could introduce her to the commands needed to launch an exe and a web site, and then just ask her to make some buttons, then add the code to those buttons, putting in her favorite web sites (facebook, twitter, etc.) and programs (iTunes, word processor, etc.) If her computer's in her room, you could also toss an alarm clock on it for added functionality. Of course, 30 minutes is too short to walk her through that, so you'd have to already have it done. At the end, you'd email a little 2-3 page user manual, the code, and the .exe to her... and then leave her with a little sales pitch: it's not easy at first, but once you get the hang of it, it's not so bad, will be extremely useful in life, and will help develop her analytical thinking.