The ability of robots to model their own dynamics is key to autonomous planning and learning, as well as for autonomous damage detection and recovery. Traditionally, dynamic models are pre-programmed or learned from external observations. Here, we demonstrate for the first time how a task-agnostic dynamic self-model can be learned using only a single first-person-view camera in a self-supervised manner, without any prior knowledge of robot morphology, kinematics, or task. Through experiments on a 12-DoF robot, we demonstrate the capabilities of the model in basic locomotion tasks using visual input. Notably, the robot can autonomously detect anomalies, such as damaged components, and adapt its behavior, showcasing resilience in dynamic environments. Furthermore, the model's generalizability was validated across robots with different configurations, emphasizing its potential as a universal tool for diverse robotic systems. The egocentric visual self-model proposed in our work paves the way for more autonomous, adaptable, and resilient robotic systems.