Sleep is critical to the health and development of infants, children, and adolescents, but pediatric sleep is severely under-researched compared to adult sleep in the context of machine learning for health and well-being. Here, we present the first automated pediatric sleep scoring results on a recent large-scale sleep study dataset that was collected during standard clinical care. We develop a transformer-based deep neural network model that learns to classify five sleep stages from millions of multi-channel electroencephalogram (EEG) signals with 78% overall accuracy. Further, we conduct an in-depth analysis of the model performance based on patient demographics and EEG channels.