"Twinkle, Twinkle, Little Star" was written by Jane Taylor (b. London, 1783; d. Ongar, Essex, 1824). It was published first under the title "The Star", and appeared in her Rhymes for the Nursery (London, 1806, p. 10). "Twinkle, Twinkle, Little Bat" is a parody by Mad Hatter in Alice's Adventures in Wonderland. The information is from Fuld's book (p. 594) and the Opies' The Oxford Dictionary of Nursery Rhymes, new ed. (Oxford, 1997, p. 474).
~Masato