The Collaborative International Dictionary of English v.0.48:

Jenny \Jen"ny\, n.; pl. Jennies.
   [1913 Webster]
   1. A familiar or pet form of the proper name Jane.
      [1913 Webster]

   2. (Zool.) A familiar name of the European wren.
      [1913 Webster]

   Jenny ass (Zool.), a female ass; also, a female of certain
      other animals.
      [1913 Webster +PJC]