Flying ad hoc networks (FANETs) play a crucial role in numerous military and civil applications since it shortens mission duration and enhances coverage significantly compared with a single unmanned aerial vehicle (UAV). Whereas, designing an energy-efficient FANET routing protocol with a high packet delivery rate (PDR) and low delay is challenging owing to the dynamic topology changes. In this article, we propose a topology-aware resilient routing strategy based on adaptive Q-learning (TARRAQ) to accurately capture topology changes with low overhead and make routing decisions in a distributed and autonomous way. First, we analyze the dynamic behavior of UAV nodes via the queuing theory, and then the closed-form solutions of neighbors' change rate (NCR) and neighbors' change interarrival time (NCIT) distribution are derived. Based on the real-time NCR and NCIT, a resilient sensing interval (SI) is determined by defining the expected sensing delay of network events. Besides, we also present an adaptive Q-learning approach that enables UAVs to make distributed, autonomous, and adaptive routing decisions, where the above SI ensures that the action space can be updated in time at a low cost. The simulation results verify the accuracy of the topology dynamic analysis model and also prove that our TARRAQ outperforms the Q-learning-based topology-aware routing (QTAR), mobility prediction-based virtual routing (MPVR), and greedy perimeter stateless routing based on energy-efficient hello (EE-Hello) in terms of 25.23%, 20.24%, and 13.73% lower overhead, 9.41%, 14.77%, and 16.70% higher PDR, and 5.12%, 15.65%, and 11.31% lower energy consumption, respectively.