A quick search of the word "taxidermy" on the state's website of images yielded these fascinating photographs. Be sure to click on them to enlarge and see all the the detail.
"Alligators were common props in photo studios and often appear in whimsical poses along with a note like "having a great time in sunny Florida," according to Larry Roberts in Florida's Golden Age of Souvenirs. So it appears that there is a long history of stuffed objects, particularly alligators, in the Sunshine State. Perhaps it was the safest way to show how wild and untamed early tourists perceived our state, while keeping the real live critters at a safe distance.
All images from the State Archives of Florida