The irony of the dragon friend.
Dragons are typically understood as enemies of men, at least in Western literature, and so many Western stories revolve around slaying the dragon, but in Minli's case, the dragon is the key to her success, and by learning to care for the dragon, she learns how to care for herself and her family.
The irony of the mountain.
The irony of the mountain is that it seems that, since it is a mountain, climbing the mountain will be in order, but no, actually, there's something entirely different than climbing that needs to be done: flying.
The mountain is an ironic symbol for flight, because it represents the fact that Minli will need help, and she'll need to fly instead of climb.
The irony of the Old Man on the Moon.
The say that an Old Man on the Moon can grant your wish is like saying that God Himself will give you what you want if you work for it. So the wish is a little ironic, since the real solution to any given problem is learned on the way to the Old Man. By the time she learned how to arrive at the moon, Minli knew enough to transform her family's fate forever, but for the purposes of allegory, a Godlike figure grants a wish. In true divine fashion, the Old Man rewards Minli for her selfless attitude.
The irony of the helpless parents.
Ironically, the parents in this story represent something of a liability, as something to be overcome. This irony helps show a greater irony, that in order to serve her family, Minli must leave them and become her own person.
The irony of the happy ending.
The transition from "Fruitless" to "Fruitful" may seem like the main goal of the story, but it's not. Since this is a children's book, the real value of the lesson is the effect the story might have if the child chooses to belief its core message, so for Minli, fortune was the reward, but for the parents, Minli herself was the reward, and the pride of having raised a winner. That's the real power of the story.
