C.P.
You have received lots of excellent advice.
My advice is to note anxiety or depression; when and for how long. Try listing all of her symptoms daily. Note routines or lack of them. Note fatigue or periods of hyperactivity. Note mood swings or lack of them. Note dietary routines, foods eaten, life stresses. This will take some effort but will slowly paint a picture that can be presented to your doctor.
Sleep disorders can produce secondary emotional and psychological secondary problems.
Your doctor either is not aware of the severity of the sleep problems or he is dismissing your concern; probably out of ignorance.
If you have a diary of sorts, you are armed with knowledge to share with a professional. If your daughter cannot wind down, cannot get into a sleep state that is normal, you will need to consult a knowledgeable professional.
First you will need a "label" and diagnosis. Then you can choose among professionals for help. For example, a GP, a sleep professional a naturopath, a nutritionist, etc.
If your daughter is very distressed by her inability to sleep, you might consider this a "crisis" of sorts and immediately consult another physician if your GP continues to ignore you.
Meanwhile, if she is not taking a good vitamin/mineral supplement, start that as soon as possible. Eliminate sugar from her diet and white flour products. Have her exercise for at least half an hour everyday, outside.
I am wondering if your daughter has a concurrent weight problem?
Good luck.
Chris RN