Early prediction of sepsis is critical for improving patient outcomes, but remains challenging due to the complex and heterogeneous nature of the condition. This paper introduces Sepsislab, a novel approach for early sepsis prediction that incorporates uncertainty quantification and active sensing. Our method addresses two key challenges in sepsis prediction: the uncertainty in predictions and the need for timely and relevant clinical measurements. By quantifying prediction uncertainty, Sepsislab provides clinicians with confidence levels for risk assessments, enabling more informed decision-making. The active sensing component strategically recommends which clinical tests should be prioritized to maximize prediction accuracy while minimizing unnecessary testing. Experiments on real-world electronic health record data demonstrate that Sepsislab outperforms existing methods in prediction accuracy, calibration, and clinical utility. Our approach represents a significant step toward more reliable and resource-efficient sepsis prediction in clinical settings.