I actually made this right before my son was born, but just recently got the pattern scanned and edited. It's been a long time coming. My son likes it so far, and I hope it'll be a toy he likes as he gets older.
You can see/print the alligator pattern here. It has 1/8" seam allowances.
First cut out all your pieces. I used green knit and red woven fabric. I think the knit made my alligator really round and a little lumpy. You can use woven for all if your more comfortable with that. Remember to mark the dots on the side pieces and the pleats on the belly piece.
The face piece will start where the seam on the top ended. I used lots of pins on the face/mouth to make sure everything lined up.