Mastering autonomous drone landing on dynamic platforms presents formidable challenges due to unpredictable velocities and external disturbances caused by the wind, ground effect, turbines or propellers of the docking platform. This study introduces an advanced Deep Reinforcement Learning (DRL) agent, Lander:AI, designed to navigate and land on platforms in the presence of windy conditions, thereby enhancing drone autonomy and safety. Lander:AI is rigorously trained within the gym-pybullet-drone simulation, an environment that mirrors real-world complexities, including wind turbulence, to ensure the agent's robustness and adaptability. The agent's capabilities were empirically validated with Crazyflie 2.1 drones across various test scenarios, encompassing both simulated environments and real-world conditions. The experimental results showcased Lander:AI's high-precision landing and its ability to adapt to moving platforms, even under wind-induced disturbances. Furthermore, the system performance was benchmarked against a baseline PID controller augmented with an Extended Kalman Filter, illustrating significant improvements in landing precision and error recovery. Lander:AI leverages bio-inspired learning to adapt to external forces like birds, enhancing drone adaptability without knowing force magnitudes.This research not only advances drone landing technologies, essential for inspection and emergency applications, but also highlights the potential of DRL in addressing intricate aerodynamic challenges.