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.
2. A state police officer; -- also called state trooper.
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.]
like a trooper, with energy, endurance, or enthusiasm; as,
to work like a trooper.