Different kids do need different amounts of sleep. My first child did not need much and when he was that age, he was not in bed before 9pm and up at 6:30. My 2nd would be in bed at 7:00pm at that age and be up at 5:30 am. So, you may just need to put her bedtime later. I realize that impacts any quiet time you might need in the evening. You might also consider whether she isn't super sensitive and some nitetime noises in the household between 7:30 and 9:30 are disturbing her sleep. Personally, if I get awakened when I'm on those early stages of sleep, it can take me forever to get back to sleep. You might consider putting a white noise device in her room (hepa air filters on low make an exceptional white noise device in our house and clean the air at the same time). Another thing to consider is what she's eating before bed. Is she getting some protein and carbs. Carbs are good because they can help you fall asleep, but some folks need protein to help maintain a steadier blood sugar level through the nite. She's too young to really know if these sorts of things are impacting her, so you may need some trial and error. Personally, I have some rice crackers with almond butter at bedtime and sleep much better, as I do have blood sugar issues. It's also possible she has food allergies such as to dairy or wheat gluten (maybe even celiac). I can use my sons as an example for the dairy, as I didn't learn until after my first was older that he had a dairy allergy. We were dairy free by the time my 2nd son was born and he has always been an exceptional sleeper and my oldest started sleeping better once he went off dairy.
Just a few thoughts from my own experiences. Good Luck!