Depends on how clever your child is. A simple latch night work for a while (hook and eye setup), until she gets the dexterity to open the latch. Shoot, even a piece of wood that you have to lift out of the way before the doors will open might work. Of course, as she grows, you have to keep upgrading the lock to something she can't handle yet, until she's old enough to be taught.
Could be worse, you could have a boy and you'd have to worry about keeping things locked up (Particularly guns and liquor) until he's out of the house. Then you get into pick-resistant locks, and all of that fun.