Is it possible for a 15 year old girl to have a IQ of 120?

Yes. Actually, IQ testing is not recommended for comparison between different age groups, since the scores must be adjusted for different maturity levels. However, it's certainly possible for a 15-year old girl to have an above-average intelligence score on standardized tests, and many do. I.Q. doesn't measure your intelligence but your ability to learn. So how smart you are is irrelevent.