There is no actual ideal body weight calculation for an 11 year old like we have for adults. Using the adult calculation, you should weigh any where from 86-105 pounds. Where you stand in that calculation would depend on your body frame size (small, medium, or large). But again- THIS MAY NOT BE CORRECT - those numbers are based on a calculation for adults.
The best way to see where you are weight-wise, for your age, is to find your BMI (body mass index) by using the equation:
weight (in pounds) ÷ height (in inches)÷ height (in inches) x 703
so you would have your weight ÷59 ÷59 x 703
This will give you your BMI. Once you have your BMI you can look on a BMI chart for girls aged 2-20. Here is a link to one:
http://www.texaschildrenspediatrics.org/healthlibrary/pa_bmigirl_art.aspx
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She should ask her doctor. There are other variables besides age and height. The BMI calculator is not a reliable way to figure anyone's proper weight (research it), unfortunately it has become the go-to chart for deciding healthy weights. The Mayo clinic has published articles on using neck diameter to more accurately determine healthy weight for children, it's worth asking a doctor about. Two girls of the same age and same height may be healthier at different weights, no matter what the BMI chart has to say about it.
At the age of 11 many girls will begin to suddenly put on extra weight as the result of puberty. This weight gain is normal.
Unfortunately, without knowing more about you, I can only suggest you look for a BMI calculator online--you can punch in weight, height, and sex and get some idea of what other girls at this height and age weigh.
Well I remember when I was 4 feet 11 inches I weighed somewhere between 85-90 pounds.