Elsie Kipling and her friends are using their imaginations to act out stories about animals in far-off lands. Not too different from how children have historically played–using furniture and blankets and other found objects to become the scenery of their world.
A good theatrical design needs to take the context of the play into account, and create a world which seems effortless and inevitable. In the case of The Just So Stories, the director first had to decide how the characters in the play would interact with the stories: would they obviously be children pretending (and letting their child-character show through) or would they, when acting out each story, become fully invested in their animal-character?
(This is not an unusual dilemma. Any time there is a “play within a play” we need to ask these questions. An O. Henry Christmas two years ago required similar decisions to be made.)