In ad hoc networks employing Autonomous Aerial Vehicles (AAVs), the importance of real-time applications and edge computing is steadily increasing. However, existing routing protocols still fail to meet the strict performance requirements under the unique conditions of AAV networks, where the network topology changes continuously, and nodes move at high speed. This paper presents SHARP-AODV (Stability Heuristic Adaptive Routing Protocol—AODV), an enhanced routing protocol specifically developed for AAV networks. SHARP-AODV introduces two key innovations: (1) an intelligent RREQ (Route Request) dissemination mechanism that combines neighbor density control with a multi-parameter probabilistic model, and (2) a multi-criteria path selection mechanism that jointly considers hop count, link quality, and resource state. Simulation results in NS-3 across four distinct mobility models and various numbers of AAV nodes show that SHARP-AODV significantly outperforms standard AODV, improving packet delivery ratio (PDR) by up to 23.9%, increasing throughput by up to 61%, while reducing end-to-end delay by up to 87.8% and jitter by up to 90.6%. The proposed protocol is especially suitable for AAV-enabled applications in Edge Computing and Metaverse ecosystems that require low-latency, highly reliable connectivity with adaptation to dynamic network conditions. Furthermore, SHARP-AODV satisfies 6G network requirements for connection reliability, ultra-low latency, and high device density, unlocking new opportunities for employing AAVs in smart cities, environmental monitoring, and distributed VR/AR systems. © 2025 by the authors.