Purpose: Estimation of patient-specific organ doses is required for more comprehensive dose metrics, such as effective dose. Currently, available methods are performed retrospectively using the CT images themselves, which can only be done after the scan. To optimize CT acquisitions before scanning, rapid prediction of patient-specific organ dose is needed prospectively, using available scout images. We, therefore, devise an end-to-end, fully-automated deep learning solution to perform real-time, patient-specific, organ-level dosimetric estimation of CT scans. Approach: We propose the Scout-Net model for CT dose prediction at six different organs as well as for the overall patient body, leveraging the routinely obtained frontal and lateral scout images of patients, before their CT scans. To obtain reference values of the organ doses, we used Monte Carlo simulation and 3D segmentation methods on the corresponding CT images of the patients. Results: We validate our proposed Scout-Net model against real patient CT data and demonstrate the effectiveness in estimating organ doses in real-time (only 27 ms on average per scan). Additionally, we demonstrate the efficiency (real-time execution), sufficiency (reasonable error rates), and robustness (consistent across varying patient sizes) of the Scout-Net model. Conclusions: An effective, efficient, and robust Scout-Net model, once incorporated into the CT acquisition plan, could potentially guide the automatic exposure control for balanced image quality and radiation dose.