Unfortunately, many female gymnasts, skaters, and ballerinas attempt to postpone their body's natural development by eating an unhealthy diet, a diet that will prevent their body from growing as it should. A diet that does not contain enough growth-producing nutrients combined with a daily regime of constant, strenuous physical activity is capable of retarding puberty. I would warn you and your friend against trying to go against nature. Undernourished, over-exercised young bodies are very prone to serious injury. In addition, it's very easy to develop addictive eating disorders in an attempt to "stay small".
Trying to delay puberty should not be your or your friend's focus. Some girls will go through puberty sooner than others will. Even after puberty, some girls will still maintain a light, short body because of their genetic makeup. Other girls' bodies will change dramatically shortly after puberty. Your friend or your figure skating success will not be determined by your postponing puberty. Your natural ability, hard work, and dedication to the sport (great coaching is a big plus too) will determine it. Ask any world-class figure skater and they will tell you the same thing. Thanks for writing.