An alligator, as distinct from a crocodile, was a predatory Earth reptile.
Alligators were commonly found in the swamps of Louisiana. (COMIC: Terror from the Swamp, AUDIO: The Coney Island Chameleon)
History
Nero threatened the First Doctor, stating he would build a moat around him and fill it with alligators. However, he changed his mind when the Doctor inadvertently inspired him to burn Rome. The Doctor told Nero's guards the punishment would be reserved for them if he and Vicki were not freed. (TV: "Inferno")
The Eleventh Doctor once encountered terrifying beast who sought to protect the population of Louisiana from alligators in 1929. (COMIC: Terror from the Swamp)
During the 22nd century Dalek invasion of Earth, many animals escaped from zoos during the plague. Most of them died, but reptiles such as the alligators thrived in the London sewers. An alligator almost attacked Susan, but was killed by David Campbell. (TV: The Dalek Invasion of Earth)
The First Doctor rescued the Chief Voord from alligators in a South American jungle. It was this act which convinced the Chief Voord to help the Doctor fight the Daleks. (PROSE: Doctor Who and the Daleks)
Similar species
Sundayan 'gators were visually similar to both Earth alligators and turtles. (PROSE: Wetworld)