I got this question in the comments of the How to Write a Children’s Book course on Skillshare.
I'm not a lawyer, so I can't give legal advice. However, I can use Google.
According to Copyright.gov, "copyright protection exists from the moment an original work is "fixed" in a tangible medium. For writers, fixation occurs when your ideas are written down on paper or typed using a computer. You don't need to do anything else for your work to be protected by copyright."