There are a number of connections which tie the moon to rabbits in Japanese folklore.
Various cultures around the world have seen different things in the moon thanks to phenomena such as pareidolia. In the west, we tend to see a man, or a face. In Japan, however, they see a rabbit.
There is an old sort of proto-science-fiction story in Japan, the oldest surviving monogatari, or work of fictional narrative prose, titled The Tale of the Bamboo Cutter, which has has been reimagined in various forms of media for hundreds of years. It’s about a girl who is discovered in a bamboo stalk, adopted by the man who finds her, and grows to become the most beautiful woman in the world. She turns down repeated suitors, and eventually reveals she is from the moon, leaving her adoptive family behind in order to return there to be with her true family. She is often called ‘the rabbit princess’ as the bamboo leafs on her head resembled rabbit ears
Just more clear references Oda is making to classical literature here