The rubber ball is a flat, featureless toy.  The Goose Prince gives it to Georgie and tells her she will be able to see the world in it.  Georgie's ability to do this, even after the death of the Prince,  signifies both Georgie's imagination and her connection to nature (because it was a gift from him).  This underscores the theme of the novel, that one must make a conscious effort to stay connected to the natural world he lives in.