This paper addresses the problem of developing a resilient load forecasting system against attacks targeting the output of a load forecasting model. To mitigate attacks on the output of the load forecasting model, a cyber-attack-resilient load forecasting optimization problem is formulated that incorporates an active defense mechanism. Based on the principles of Moving Target Defense (MTD), the active defense mechanism employs a switching structure to continuously and dynamically change the currently active predictor, thereby preventing the attacker from successfully identifying the forecasting system. The unpredictability of the proposed load forecasting system is quantified by measuring the largest component of the information entropy generated by the switching mechanism. A Deep Q-Network (DQN) agent performs the switching based on maximizing the accuracy achievable by the predictors while simultaneously maximizing unpredictability. In this way, a desirable trade-off between forecasting accuracy and unpredictability is achieved. This trade-off is determined by an optimization weight, which represents the weight assigned to the unpredictability term in the optimization problem. Without loss of generality, a data integrity attack is applied to the output of the ANN predictor. Simulation results demonstrate the advantage of the proposed approach in mitigating the impact of the attack while simultaneously accounting for forecasting accuracy, rather than merely improving the accuracy of the proposed framework relative to attack-free models. The configured load forecasting system performs well in the absence of an attacker and mitigates the impact of the attack when an attacker is present.