In the last post I'd mentioned in passing the Indian tale of Lord Indra rewarding the sacrifice of a rabbit, which I'd never heard before and found touching. Looking for details, I turned up some more rabbit - moon links in an old book review:
The Hindus called the moon casin, or Sasanka, " Marked with the Hare," from the story of Sakya-muni (Buddha). This holy man in an early stage of his existence was a hare, and, when in company with an ape and a fox, was applied to by the god Indra, disguised as a beggar, who, wishing to test their hospitality, asked for food. All went in search for it, the hare alone returning unsuccessful; but that he might not fall short in duty to his guest, he had a fire built and cast himself into it for the latter's supper. In return Indra rewarded him by a place in the moon, where we now see him. Other Sanskrit and Cingalese tales mention the palace of the king of the hares on the face of the moon; the Aztecs saw there the rabbit thrown by one of their gods; and the Japanese, the Jeweled Hare pounding omochi, their rice dough, in a mortar. Even the Khoikhoin, the Hottentots of South Africa, and the Bantus associated the hare and moon in their worship, and connected them in story, asserting that the hare, ill treated by the moon, scratched her face, and we still see the scratches. Eskimos think the moon a girl fleeing from her brother, the sun, because he had disfigured her face by ashes thrown at her; but in Greenland the sex of these luminaries is interchanged, and the moon pursues his sister, the sun, who daubs her sooty hands over his face. The Khasias of the Himalayas say that every month the moon falls in love with his mother-in-law, who very properly repulses his affection by throwing ashes at him.
--from Star Names and Their Meanings by Richard Hinckley Allen (New York: G. E. Stechert, 1899), reviewed in The Critic, vol. XXXIV no. 859, January 1899, p. 574.