Effective Edge AI for space object detection (SOD) tasks that can facilitate real-time collision assessment and avoidance is essential with the increasing space assets in near-Earth orbits. In SOD, low Earth orbit (LEO) satellites must detect other objects with high precision and minimal delay. We explore an Edge AI solution based on deep-learning-based vision sensing for SOD tasks and propose a deep learning model based on Squeeze-and-Excitation (SE) layers, Vision Transformers (ViT), and YOLOv9 framework. We evaluate the performance of these models across various realistic SOD scenarios, demonstrating their ability to detect multiple satellites with high accuracy and very low latency.