There aren’t very many studies reporting on the number or rate of injuries among ballet dancers. From the little bit of information reported from professional dance companies, it seems that injuries are very likely.
Most of the injuries are in the legs and back as a result of overuse. Repetitive motions during long hours of training are common before injuries develop. There are cycles of injuries based on the dance calendar. For example, there is a higher rate of injury at the start of the dance calendar and around the time of a performance. For students, injuries also develop during the training cycle with ballet exams.
If your daughter is dancing for fun and enjoyment rather than in a competitive mode, then she is not as likely to be injured. Most ballet instructors require each girl meet certain benchmarks of development before going en pointe. For example, they must be menstruating, have sufficient standing leg turnout, and ankle strength.
There doesn’t seem to be a place in the ballet world for girls between the ages of 12 and 18 who don’t want to train en pointe. If you decide to direct your daughter in other ways, modern, jazz, hip-hop, and tap are alternative options that may be acceptable. There are injuries with any type of dance. But the rate of injuries for these forms of dance remains unknown.