Update: This pattern on About.com (now "The Spruce") looks very similar:
Web archive pattern link:
You can pick up a Brother cs6000i sewing machine on Amazon here (the one I use):
Original pattern was from "compulsivecraftiness.com" but the site no longer exists.
Web archived page: https://web.archive.org/web/20140924211940/http://compulsivecraftiness.com/2012/cozy-fleece-dog-coat-tutorial/
Thanks to "Compulsive Craftiness" for making a nice pattern and set of directions. I followed them closely and ended up with a nice little coat for Gracie. In the future I might design my own now that I have a general idea of the process. I made the top of the coat sharks because she is sometimes like a little shark right now (still has her baby teeth).