This paper studies high-speed online planning in dynamic environments. The problem requires finding time-optimal trajectories that conform to system dynamics, meeting computational constraints for real-time adaptation, and accounting for uncertainty from environmental changes. To address these challenges, we propose a sampling-based online planning algorithm that leverages neural network inference to replace time-consuming nonlinear trajectory optimization, enabling rapid exploration of multiple trajectory options under uncertainty. The proposed method is applied to the drone interception problem, where a defense drone must intercept a target while avoiding collisions and handling imperfect target predictions. The algorithm efficiently generates trajectories toward multiple potential target drone positions in parallel. It then assesses trajectory reachability by comparing traversal times with the target drone's predicted arrival time, ultimately selecting the minimum-time reachable trajectory. Through extensive validation in both simulated and real-world environments, we demonstrate our method's capability for high-rate online planning and its adaptability to unpredictable movements in unstructured settings.