Yes, each enemy you kill gives you REP. Once you are more confortable playing and using your weapons then you can review the REP guide here to be more efficent at using those weapons for more REP.
As a Level 10 needing to kill L15 Navy (I'm assuming its your doll or TP quest) the game is designed to 'slow you up a bit' to force you to catch your weapon and noriety levels up some...
And don't try to go too fast - it ends faster than you think
Also - when neeing one or two tough items try to crew up in game or come here to the Guilds and Crews Forum, post your name, time, server and place with a help request, and someone will usually meet up with ya and help with the items