I just checked.The Florida Fish and Wildlife Conservation Commission has kept records of alligator bites dating back to 1948. There have been 383 alligator bites on people in unprovoked encounters. Of the 383 total incidents, 23 of those were fatal, with 16 of those deaths being children aged 2 to 4.
So, it's very rare, but still way more than I would have thought. I would have guessed maybe 5 toddlers in the last 100 years.