The Collaborative International Dictionary of English v.0.48:

Whimling \Whim"ling\, n. [Whim + -ling.]
   One given to whims; hence, a weak, childish person; a child.
   [1913 Webster]

         Go, whimling, and fetch two or three grating loaves.
                                                  --Beau. & Fl.
   [1913 Webster]