I don't think I could summarize the story any better than the back cover. Forgive the awkward translation, but I just didn't want to lose anything.
“The immortal story of Herman Melville about a big white whale is presented anew in a new adventure of little Moby Dick.
“The story begins during the year of 1841, when glorious ships sail the seven seas. But deep in the ocean is another world, in which the shy orphan whale by the name of Moby meets his friends – starfish Stella and sea horse Winnie. The two of them encourage Moby to overcome his fears by showing him their underwater world including some of the strangest sea creatures. But on the surface are many dangers, particularly the ruthless Captain Ahab, who will stop at nothing to catch the biggest miracle in the sea—a white whale. Moby must come face to face with him in order to take his place as lord of the sea. One story, showing the joy of life and the magic of friendship.”
As you can see, The Adventures of Little Moby Dick is another of those post-modern re-tellings of canonical tales re-inventing previously vilified or undeveloped characters such as Wicked, Rosencrantz & Guildenstern Are Dead, and Ahab's Wife. Of course, to say that Moby Dick was previously undeveloped is absurd. And it remains open debate how you can have a post-modern take on an already so thoroughly post-modern novel. However, it does illustrate the depth of Melville's world that it can support such further stories, even ones that contradict the events recounted in The Whale. Of course, we have no idea from Melville whether Moby had starfish and sea horse friends, and in all likelihood, he did. Did Ahab really kill Moby's mother and is this the true source of the enmity between them? The movie brings up more questions than it answers, but I must say that the movie brings the story to a more natural conclusion when Ishmael and Moby become friends and sail the seven seas together.