Oliver and his Alligator (Paul Schmid)

Kids are so funny. When I read this book to my class no one baulked at the idea that a kid would pick up an alligator on his way to school. Actually, that's a perfectly reasonable way to deal with a day that you're nervous about! Who couldn't use an alligator to eat up all your fears?!

Goodreads summary:

Oliver is nervous about the first day of school, so he picks up an alligator at the swamp, just in case. And boy, does it come in handy! Whenever anything scares Oliver--be it a teacher, a classmate, or the prospect of learning "everything"--the alligator makes the problem go away. Quickly, school becomes much simpler . . . and a little lonely. But Oliver knows just what to do! Paul Schmid's gentle, funny tale about overcoming first day of school jitters is destined to become a modern classic that fans of "Olivia" and Kevin Henkes' books will love.