Piling on with the lockbox idea, doesn't have to be expensive or fancy, just something to keep little prying fingers away. The LifeJacket item might work well for you.
Also, pick up a copy of Massad Ayoobs excellent pamphlet, "Gun Proof Your Children".
Come clean about it, tell her one of your main concerns was HER safety and the safety of your child. Get her involved if you can. Also, since this is your first handgun, prove to her you mean it about being a safe and responsible gun owner by getting some good local training, starting with the NRA Hunter Safety course and moving up.
