The history of the Jackalope depends largely upon who is spinning the tale. Jackalopes are mythical creatures, and thus their history is like a folklore based on the origin of the myth and those who continue to perpetuate their existence to the gullible.
One such slinger of Jackalope bull shall be known as Grandpa Larry. Grandpa Larry had a stuffed taxidermy in his bedroom prominently displayed for all to enjoy. What the creature actually was, was a stuffed Jackrabbit with antlers from a tiny deer mounted to its skull. Larry had a taxonomic Latin name for this creature which was Lepus Ungula. The word Lepus represents the rabbit part of the creature, but ungula was a bit more puzzling as it means hoofed. Clearly, Grandpa Larry's Jackalope did not have hoofs. Grandpa Larry when challenged on this would simply state that this particular Jackalope was not an evolutionary anomaly, but had been captured before its hoofs had developed.
Grandpa Larry would go into elaborate detail about how radiation from testing for the atomic bomb and dumping of nuclear waste in the Nevada desert caused this genetic freak to come into existence. Whenever one of Larry's grandchildren would bring over a friend to meet their beloved Grandpa, he would seize the opportunity to make a new victim of his BS when they would ask about the taxidermy.
Grandpa Larry was an expert and historian on the Lepus Ungula. He would tell people about their nocturnal nature, and their unusual feeding habits. He would put fear into kids by telling them that they preyed upon small children and pets. He told of how their eyes would glow in the dark.
Somehow, Grandpa Larry seemed to make his story quite believable. He had an answer for every conceivable question a person could think of regarding things Jackalope. He knew about their breeding habits, their gestation period and he could mimic their unusual mating call.
When someone would raise an eyebrow of disbelief, Grandpa Larry would ask them " What's not to believe ? You have eyes, you can see for yourself how real the Jackalope is. Because of the radioactivity, he would discourage touching.
The Grand-kids would be always amazed at the high percentage of people who would leave Grandpa's house as Jackalope believers, and they would delight in bringing him new disciples of his hogwash. Occasionally, even a non relative would bring someone by to hear the story which would take on a life of itself and evolve almost as quickly as the radioactive bunny did.