Well, it should show up in your data tab in the launcher. If it is there and checked then it is installed. If you start the game up and you encounter the courier that starts the mission, you know it is installed correctly.
Ok, yeah I can forge 24 arrows. I didn't know that was a Dawnguard thing. I've never been through the whole game. I'm going through it now recording my playthrough so I wanna make sure I know what's going on.
For epic viewing fun, start right here: http://www.youtube.com/watch?v=F15u5YdzN8E&feature=plcp