Kids' Sewing Machine

You could go ahead and buy a regular sewing machine, sometimes the lower-end ones are less than $80. Sears, Walmart, Costco, and craft stores usually have them where you can look at them. I got a good deal on one from HSN. It was a Europro brand, and had a nice storage case built in. It did break though, because when my son was little he put pins inside the moving parts. After that I bought a basic brother machine.
My son is now 8, and he knows how to use the regular sewing machine. To be safer, he likes to either turn the wheel by hand, or use the button that does a single stitch at a time. Because there are dotted lines and arrows printed right on the machine, he can do all of the threading except the last step of going through the needle. He can wind a bobbin and put in the drop-in bobbin. But if it gets tangled, he needs help.
We cut up old tshirts into 6 inch squares, and he sewed on yarn and other decorations. I sewed them together to make a very special quilt for him.

I'd suggest either find a friend with a sewing machine that don't use (I know a ton of girls that intend on sewing, but the machine sits in their closets)who would be willing to let you loan or purchase for cheap. That way you can test out if sewing is for her. I would also suggest getting lessons or search on youtube how to sew. Read the manual if you have it on proper threading. I have the 30 year old kenmore that we got at a thrift store and I thought I knew how to thread it. . .no. Read it like a bible. But it's the best sewing machine I've ever used. And we are talking I've used about 30-40 different kind of machines.
Dont have her start with knit fabrics. Worst idea ever! (my sewing teacher in middle school had me learn with knit!!!) have her start with a cotton callico or 100% cotton that is super easy to learn with. You don't want to learn on polyester because of how it can pull and snag.

We bought a Babylock for our 15 yr old. We got the same model that is in the Plano schools. It has to be sturdy and easy to use for students.

Daughter loves it. We paid about $375 for it. It is worth it. You get what you pay for. Plano Sewing Center has classes as well.

As a seamstress myself, I can recommend the Janome (ju-no-mee) Mini like this one with a 25 year warranty: http://cgi.ebay.com/Janome-Sew-Mini-Sewing-Machine-11703-...

OR

A Brother machine with a 25 year warranty like: http://cgi.ebay.com/Brother-Sewing-Machine-VX-1435-/38024...

Also, consider taking a course in sewing with your daughter like the video course offered by Modesty Matters. (http://www.modestymatters.net/limitedtimeoffer.php) It is a comprehensive course that will make sure that she doesn't have any "gaps" in her technique which will obviously enable her to shorten the learning curve and take her imagination further faster. It makes for a great, self-paced, mother-daughter course on weekends or over the summer, or at night, or whenever!

Best Wishes!