Gator by Randy Cecil

From the back of the book:
Gator loves everything about being a carousel animal, and most of all, he loves the laughter. But day by day, fewer and fewer people come to the amusement park until one day, no one comes. Thus begins a most touching odyssey, as Gator leaves behind the only life he's ever known and sets off through a dark forest, to a place with real alligators - and a wonderful, familiar sound.