The complexity and unpredictability of disaster areas pose significant challenges to post-disaster rescue operations. UAVs, with their flexibility and rapid response capability, are able to perform various tasks and provide critical field data. However, these tasks are often computationally intensive and have strict latency requirements, and UAVs have limited computational resources. Therefore, effectively handling a large number of real-time tasks becomes a significant challenge. To address this, we propose a solution combining UAVs and mobile edge computing to optimize task processing. We focus on UAV-assisted task computation in post-disaster scenarios, considering indivisible and latency-sensitive tasks, and construct an edge computing framework for task offloading. We propose a deep reinforcement learning-based task offloading algorithm (TODRL), which predicts UAV loads using LSTM and adjusts offloading strategies with Dueling DQN to minimize latency. Experimental results show significant latency reduction compared to traditional methods, validating the approach’s potential and effectiveness in post-disaster rescue.