I'm with you guys,
ONE dead deer, that MAY or may not have been poached > doesn't sound to me like ma cat problem at all
NOW if you were finding a LOT of dead animal remains all over, then I would say you have a problem

your goat getting killed, is again sad and sucks, but having animals in an area where predators live, happens, its part of the game, its like farmers that get crop damage, its expected, and unavoidable
NOW if you have excessive amounts of crop damage or, live stock being killed, THEN you have a problem(or finding a LOT of dead animal remains) till then, you sound like you just have a mix of natural wildlife in your area
if its legal to hunt or trap, have at iot, not one to say not to if it makes you happy
But I doubt you have a true problem there?
your IMO jumping the gun on your conclusions based on one dead deer, of unknown death
PLUS you THINK possibly poached, , which to me would be a bigger worry if your having poachers killing your game!, poachers IMO
do more damage than natural predators do by far!