Federated Learning (FL) has demonstrated promise for collaborative training on decentralized data while preserving privacy. However, applying FL to object detection remains challenging due to non-IID data distributions and domain shifts that can degrade performance with standard aggregation methods. To address these issues, we propose the Uncertainty Incorporated Federated Learning for Object Detection (Unify) framework, a novel FL framework that leverages Evidential Learning (EL) to estimate both epistemic and aleatoric uncertainties. By integrating these uncertainty estimates into the aggregation process, Unify down-weights unreliable client updates, leading to improved cross-domain generalization and enhanced stability. Built upon a lightweight YOLOX detector, our approach achieves detection performance that closely approaches centralized training while significantly outperforming conventional FedAvg under heterogeneous conditions. Evaluations on the KITTI and nuImages datasets demonstrate that Unify improves mean Average Precision (mAP) and yields uncertainties. The findings highlight the potential of uncertainty-incorporated FL in developing resilient, adaptive, and self-organizing computing systems.