There are certainly aspects of all three in this story. Since you ask specifically about fables, I'll talk about that.
A fable tends to involve animals acting in anthropomorphized ways. The things the animals do teach us something about our own lives, societies, etc. In this book, the animals' actions teach us a number of things. We learn, most importantly, that it is very difficult (perhaps impossible) to create a utopia in which no one will be exploited. This is one of the morals of this story.
So, since you have animals acting like people and a story that teaches us a lesson, you have aspects of a fable in this book.