It is true that these partial awakenings do tend to happen within the first few hours after having fallen asleep. They occur from deep, non-dreaming sleep. During the event, your child gets up abruptly and then may stare, look upset, and appear confused. These can be accompanied by sweatiness and fast heartbeat. These confusional arousals usually last only 5 - 20 minutes. They simply run their course as your daughter settles down and goes back to sleep. Fortunately, she is not actually awake and should not have any recollection about these episodes in the light of day.
Try to relax -- only your own sleep is being disrupted a bit. If they are occurring too often, talk with your daughter's doctor. There are possible, much less commonly used alternative treatments such as waking her before the episodes usually occur or very rarely using a medication to help provide temporary relief for the family. Your daughter's doctor can let you know what is best for her.