The Wikipedia article on Jackalopes has references to the complete history and origin of this mythical creature. Other websites such as Jackalopes!, Legend of the Jackalope, and The Jacaklope Conspiracy paint a much more fanciful image. However, for the purposes of Furry Fiesta, a jackalope is a jackrabbit with a bit of antelope mixed in. Hence it's appearance as a jackrabbit with antlers. Like this:

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Furry Fiesta's family of Jackalope mascots is comprised of the dashing Jack, the lovely April, and a whole herd of wild jackafluffies.