I'm not a father or a girl...
but I know my younger sister has some views on those things. Our father taught all of us to shoot, and we do it pretty well. She wasn't as into it as much as us boys mostly because of my father's teaching method. She shoots with me alot now. She seems to like her SKS, being a college student it's cheap on ammo and kinda cool.
But on to the point. I'd just give her a try with the .380 and see what works. A .22 revolver might be a good idea if she can't get good groups with the 380. I think it has more to do with what someone is comfortable with than actual recoil properties. My sister used to shoot a .44 Magnum on occasion at that age. She just had to hang on tight.
That said, good luck on the endeavor. I enjoy teaching women to shoot because they do better at it than alot of men starting out. My personal belief is that it has to do with them having no preconcieved notions and better fine motor control.
I always recommend some flavor of .22 for a first gun.
I always recommend some flavor of .22 for a first gun. They have virtually no recoil, low noise, and are cheap to shoot, inexpensive to buy, come in so many configuration's that you can find one to fit anyone, and as it does not break the bank to go and buy 500 (a brick) of rounds that will last a whole day at the range and they will shoot more. Once they get comfortable with the .22 let them decide what they want.