I cannot vouch that this is the original version but the poem appears in
St. Nicholas Magazine (Vol. 2 No. 8 Page 471) issued June 1875 and titled "The Little Girl Who Would N't Say Please" by M.S.P.
St. Nicholas: Scribner's Illustrated Magazine for Girls and Boys
Whilst researching this I found reference to a picture book from 1910 titled "Little girl blue lives in the woods till she learns to say please" by Josephine Scribner Gates. It is interesting to note that she shares a surname with the publisher of St. Nicholas, Charles Scribner, but appears to be of no familial connection.