After my previous post in which I showed how I made doll "stuffies", a reader asked what kind of fabric I used. It is a commercial product which I ordered online, called Inkjet Fabric Sheets. If you click on that link, you will see that the packaging has changed since I bought the product (pictured below) two years ago, but it's the same item.
It is just cotton fabric stuck to paper. You feed it into your inkjet computer printer and print your image as if you were printing on paper. After printing, you peel off the paper and--voila!--you have printed your picture onto fabric. It is no different than printing on paper, except that it costs more (the cost of the product plus shipping makes it around $1.50 per sheet).
You can get the exact same result by ironing freezer paper to white fabric. There are several on-line tutorials explaining the process, such as the one at Craftionary. It would be a little more work, but I'm sure it would be cheaper. I hope you make something amazing!