Do you want it redesigned or merely reproduced in a different format?
If you're happy with the design of the logo, there are a number of programs that could convert it to a vector format - these include Corel Trace (part of the full Corel Draw package) and Adobe Streamline.
Meanwhile embroidery digitizing programs will accept the raster image as input. Someone in this newsgroup or alt.binaries.crafts.pictures might even be willing and able to do a version for you directly from the .jpg graphic on your web page (although it's a little small to work with easily ? a full-size un-compressed scanned image would be better to work from, and this would be true if you wanted to vectorize it yourself, too.
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All logos and trade names are the property of their respective owners.