Hello, and I hope I can help you today.
The hard middle part bulging underneath your daughter's labia is possibly a condition called an imperforate hymen
. Normally, when a girl begins to menstruate, there is a small hole in the hymen that allows the blood to pass. Considering that your daughter is beginning to develop pubic hair, it is possible that she has begun to menstruate. However, with an imperforate hymen (meaning there is no vaginal opening) blood can build up inside her vagina which eventually fills the vagina with blood and cause a bulge to appear at the vaginally opening, pushing the labia open. It is also possible that your daughter does not have a properly developed vagina, which is something girls can be born with, also causing a bulge at the vaginal opening.
Either way, your daughter will not be able to menstruate normally if she has either of these conditions.
I would recommend bringing your daughter to a gynecologist for examination. Children can easily be examined by a gynecologist by going on their hands and knees on the exam table and being examined from behind. An internal examination is rarely necessary to make a diagnosis. If your daughter does turn out to have an imperforate hymen, a small simple operation can be performed to make a small hole so the menstrual blood can drain. In addition, the doctor would be able to reassure you whether your daughter's anatomy is normal.
I hope that I was able to adequately answer your question today, and that you are able to find the proper diagnosis by seeking appropriate care for your daughter from a gynecologic specialist.