No idea how bad your depression is, but, I've had very severe depression, especially recently. Not about hair loss (though I worry about that too of course, or else I wouldn't be here), but other stuff. I've been on Prozac for a couple months now. I haven't noticed any extra hairloss really, aside from shedding which I'd attribute to Rogaine (started about a month ago).
While I agree excercise is something you should definitely do (I work out daily, and I have swim practice every day), if your depression is anywhere near as severe as mine, excercising won't make it all better. But, that could just be me, since I have OCD, I obsess about certain things. Prior to the Prozac, working out would either take my mind off it temporarily (it would come back right after the work out) or it wouldn't do anything at all.
Point is, I wouldn't attribute any of my hairloss to Prozac. I'm not aware of my chemical body functions though, so, I have no idea if on some level it is or isn't affecting my hair.