The best way to animate any living thing is to observe. Rent movies with alligators, watch TV shows with alligators, go to the zoo, borrows books at your library, and so on.
Also, you can try to find tutorials on a 4-legs walking cycle.
Notice that there is 4 states in any walking cycle. You can then loop your keyframes.
Finally, make a lot of sketches, showing the alligator in different positions. Especially when you watch a show, sketch as quickly as possible the movement, only with skeleton lines.
When preparing animation, you never observe too much.
Bernard Lebel