Flying Ad Hoc Networks (FANETs) face significant challenges in maintaining stable communication links due to high mobility and dynamic topologies. This paper proposes Energy and Link Stability Aware routing protocol (denoted ELSA), a Q-learning-based routing protocol that optimizes routing decisions in real time using metrics like link quality, residual energy, flight direction similarity, and proximity to the destination. Each packet acts as an agent, selecting the best next hop among neighboring UAVs by learning from interactions with the network environment. This approach ensures routes are chosen based on both immediate conditions and long-term stability, enhancing reliability. Simulations conducted in a 3D UAV environment show that ELSA achieves a 96% packet delivery ratio, surpassing AODV (85%) and DSR (78%). Additionally, ELSA reduces the end-to-end delay to 30 ms compared to 45 ms and 50 ms for AODV and DSR, respectively, while lowering energy consumption by 20% relative to the baseline protocols.