It really depends on the development of the player and not necessarily age.
We all know girls develop faster than boys but that does not mean at 12 or 14 the ladies are ready for full weight training.
It is always wise to have a physical and inform the physician prior to any change in activities. Other factors to consider before starting a weight training routine is she on a nutrition plan? Has she been doing a polymeric, agility and stretching routine regularly?
I started my DD at 11 using cones, ladders for agility training. Jumping rope, using a squeeze ball, medicine ball drills, stretch tube drills and some light dumb or kettle bells, pushing and pulling sleds at
http://adrenalinesf.com/. It was agreat place and they will cater to sport specific workouts so look for a place that does the same.
After a year using this equipment and drills "done correctly" you should see considerable improvement in strength and development. You do not need to stay with Adrenaline or any trainer forever just long enough to learn the drills and routines.Then she would be ready to move onto more weight training if she wants to do it.
At 13 my DD wanted more of a one on one and more pure weight training so she went to BEAT
http://www.dietandexerciseguru.com/?p=845
They did regular blood work and built a plan for her that she followed through high school.
At college they had their own system but they did adopt some of the training methods she had learned over the years.
I would caution you about your HS weight training... a lot of bad things can happen there. Watch having her do "squats". I am not a fan of bulk squats and in the HS gym this is where a lot of knee injuries happen.
"Google" Caitlyn Trout and watch her form, This is key...Do not worry about "a lot of weight" the weight and power will come in time… By the time she was in HS even if she mis-hit the ball she had enough power to drive the gap or through the infield.It also helped her be more athletic behind the plate, built endurance etc.
BEAT also has a good interview about building power but keeping a good cut female body…
http://www.beatpersonaltraining.com/videos2/