Obstacle avoidance is a key feature for safe Unmanned Aerial Vehicle (UAV) navigation. While solutions have been proposed for static obstacle avoidance, systems enabling avoidance of dynamic objects, such as drones, are hard to implement due to the detection range and field-of-view (FOV) requirements, as well as the constraints for integrating such systems on-board small UAVs. In this work, a dataset of 6k synthetic depth maps of drones has been generated and used to train a state-of-the-art deep learning-based drone detection model. While many sensing technologies can only provide relative altitude and azimuth of an obstacle, our depth map-based approach enables full 3D localization of the obstacle. This is extremely useful for collision avoidance, as 3D localization of detected drones is key to perform efficient collision-free path planning. The proposed detection technique has been validated in several real depth map sequences, with multiple types of drones flying at up to 2 m/s, achieving an average precision of 98.7%, an average recall of 74.7% and a record detection range of 9.5 meters.