I did a quick search for "ink jet fabric" and this was the first link I found. It looks like one of these options should do the trick for you!

Even a largish office supply store will have the printable iron-on transfers, usually HP brand.

And you can check here also..

Here is a link that might be useful: http://www.vintageimagecraft.com/transfer_images_fabric.html

Michael's has printable fabrics. Look in the t-shirt decorating section. The sheets are letter size - 8.5 X 11, but you could put fabric strips on the sides to make the pillow top larger.

I looked into the various possibilities last summer when I was doing something similar.

I knew I could count on this forum to come up with some suggestions. The first thing I'm going to try is one of the ideas from vintage image craft, using parchment paper and my own fabric. If this doesn't work, I'll look for some of the printable fabrics.

I did a little research on my own, too. I came up with a product called Omni-Gel, a photo transfer liquid. However, it looks like I can only get it on-line from JoAnn's. With this, I think I can transfer the image to a larger piece of fabric and avoid having to do any piecing, but I'm so anxious to get started on this project, I think I'll give the parchment paper a try. I'll let you know if it works.

In the meantime, if anyone has ever used the Omni-Gel, I'd love to hear from you.

I was wrong when I said parchment paper. It's freezer paper, which I did use, but boy, my printer did NOT like the fabric and paper combination.

On to plan B.........find the printable fabric.

If your printer could not handle the fabric with freezer paper ironed on it, it may not handle the printable fabric either as it is very similar. You might want to open the package when you find it to see if you think your printer can handle it.

I was going to try something similar using a PhotoEZ silk screen kit...was trying to figure it out without buying the entire kit though. Anyway, here is the link (I have nothing to do with the company).

Here is a link that might be useful: PhotoEz Starter kit

Dritz tracing paper.

You could get it done at Spoonflower. Check out the link below.

Spoonflower custom prints fabric, from your design. It might be a bit pricey for just one pillow.

Here is a link that might be useful: Spoonflower

Thanks everyone for all the ideas. I've learned about many different ways to transfer images to fabric! I'm happy to report that I found the printable fabric and that, more importantly, it agreed with my printer! Originally, I thought I wanted to enlarge the back of the postcard to fill the entire 12X16 pillow, but after being limited to the size of the printable fabric (8 1/2X11), I ended up just color copying the postcard in its original size. I'm very happy with how it looks. Now I just have to figure out how I want to add it to the pillow and whether or not to add any embellishments. I'll try to post a picture when the project is complete.