The Collaborative International Dictionary of English v.0.48:

Trooper \Troop"er\, n.
   1. A soldier in a body of cavalry; a cavalryman; also, the
      horse of a cavalryman.
      [1913 Webster]

   2. A state police officer; -- also called state trooper.
      [U. S.]
      [PJC]

   3. A mounted policeman. [Australia]

   Note: The black troopers of Queensland are a regiment of
         aboriginal police, employed chiefly for dispersing wild
         aborigines who encroach on sheep runs.
         [Webster 1913 Suppl.]

   4. Trouper.
      [PJC]

   like a trooper, with energy, endurance, or enthusiasm; as,
      to work like a trooper.