I think the moral of this story is also about fairness. The little red hen offers the other animals the chance to help at each stage of making the bread. Since they decline, it's only fair that they don't get to share the bread. It implies that in life, if you don't contribute, you don't deserve to benefit.
Well, the moral could be seen as self - reliance too. The little red hen doesn't rely on the other animals to do the work. She plants the wheat, harvests it, mills it into flour and bakes the bread all by herself. This shows that we can achieve things on our own if we are determined and hard - working, instead of waiting for others to do things for us.