I checked with both Web sites that had the poem posted. One said they found it attributed to "anonymous" in a book dated 1918. The other found it attributed to Eliza Lee Follen in a book published in 1914. A previous attribution to Mary Howitt was found to be incorrect.

Some sources say that Eliza Lee Follen wrote "Three Little Kittens," but I found it was attributed to "anonymous" in a collection edited by Follen. I think the same may be true of "New Moon," so I'm reluctant to attribute it to Follen. Whatever the case, it was written before 1914, so there is no copyright problem.
-Joe Offer-