We present a data-efficient algorithm for learning models for model-predictive control (MPC). Our approach, Jacobian-Regularized DMD (JDMD), offers improved sample efficiency over traditional Koopman approaches based on Dynamic-Mode Decomposition (DMD) by leveraging Jacobian information from an approximate prior model of the system, and improved tracking performance over traditional model-based MPC. We demonstrate JDMD's ability to quickly learn bilinear Koopman dynamics representations across several realistic examples in simulation, including a perching maneuver for a fixed-wing aircraft with an experimentally derived high-fidelity physics model. In all cases, we show that the models learned by JDMD provide superior tracking and generalization performance in the presence of significant model mismatch within a model-predictive control framework, when compared to the approximate prior models used in training and models learned by standard extended DMD.