I would build it the same as a regular bookshelf as some children's books are rather tall. Make sure it is secured so it won't fall over on them. I built our book shelves out of shelving board and then put a back on them from plywood. I glued and added nails to secure the boards in place.
Use crates from Michaels and screw them together.
This may work: https://www.hometalk.com/29222648/children-s-book-shelf-up-cycle
Make it small, interesting and colorful.