You need to check your state regulations first. Then go from there. Here, .243 is the minimum.
.243 was my first deer rifle. Of course, I was no where near petite at 13 years old...but I had no problems shooting the .243 caliber.
I would get the .243 just because of more power, and not that much difference in recoil. Get her a heavier gun (to reduce muzzle jump) and get her a good recoil pad. She should be fine.