Foremost; Get her a left handed gun.
Make sure the butt stock of the gun fits her size (as in length). Some stocks are made too big for smaller stature people. A first gun that doesn't physically fit the shooter will sour someone to shooting rifles.
Put a good scope on the gun. Four power is fine for most hunting under 150 yards. A bolt action .270 with 130 grain loads is excellent for deer and not harsh on recoil.
My first deer was taken with a .270 when I was six years old. It was with mild hand loads that my Papa loaded up. I used a Remington 760 pump, 4x scope, with a cut-down stock that fit my size. That was in 1966.
LEO, NRA member, Native Texan. Shooting and hunting for over 45 years!