It works now. "The alligator lives, doesn't it?" sounds an unlikely and unnatural sentence.
There are all sorts of living beings for which it sounds strange in English to use "he" or "she". Snakes, butterflies and fish, for example.
In my native language nouns are: male (masculine), female or neuter; it doesn't matter are they - human, animals, things, plants... weather, seasons... But animals are always he or she, to call them "it" it would be very strange, you can call it only if you despise them, or something like that.