The integration of Unmanned Aerial Vehicles (UAVs) with Mobile Edge Computing (MEC) expands coverage and flexibility in low-altitude networks, enabling next-generation Ultra-Reliable Low-Latency Communications (URLLC). However, deep fading and air–to-ground channel fluctuations increase task transmission latency and degrade offloading reliability. To overcome these challenges, we propose an online resource management scheme deploying Fluid Antennas (FAs) in a UAV-enabled MEC network to mitigate propagation impairments and enhance the Quality of Service (QoS). Specifically, we aim to minimize the total energy consumption of MEC users and the UAV while meeting FA port constraints, UAV speed limits, per-user QoS guarantees, and queue-stability requirements, thereby delivering enhanced URLLC service. By leveraging Lyapunov optimization, the original stochastic problem is transformed into a series of deterministic per-slot online optimization subproblems. A Block Coordinate Descent (BCD) algorithm then decomposes each subproblem into three tractable components. Closed-form solutions are derived for computing resource allocation and uplink time-slot assignments, while UAV trajectory and FA port selection are optimized via low-complexity Successive Convex Approximation (SCA) and Projected Gradient Descent (PGD) methods. Simulation results show that the proposed algorithm significantly reduces energy consumption compared with existing benchmarks, maintains queue stability, and delivers superior URLLC performance in multi-task and dynamic scenarios.