I thought about it for a long time to be honest. I wouldn't let my kids near anything that involves pointing a gun at someone, they're just too young. They've been given access to the xbox, where it's a game I can play along with them, or something that they need to think about to play - puzzles and stuff that requires lateral thinking. They're also strictly limited to the weekend for gaming, it just interferes with homework otherwise.
Before I ever had kids I watched my nephew turn into a little vegetable playing hours and hours of PS2 games from the age he could hold a controller, and it scared the hell out of me. I have one particularly vivid memory of him kicking the crap out of a bystander repeatedly in GTA. He's in his teens now and has serious concentration issues, to the point that he has to have someone beside him in exams to keep him on track.
Quite possibly a completely separate issue, but it scared the bejeesus out of me nonetheless. I don't even let my kids SEE me playing shooters or anything remotely violent.
I agree. I've got a 2 1/2 year old son and I don't let him see me play games, let alone allow him to play. I know he's half the age of the OPs daughter, but I can't see my policy changing for a few years yet.
If you want her to play something, have a look on the CBeebies website for a general idea of the types of games which are recommended. I don't think you will find many shooters, however.