Quantum networks are expected to become a key enabler for interconnecting quantum devices. In contrast to classical communication networks, however, information transfer in quantum networks is usually restricted to short distances due to physical constraints of entanglement distribution. Satellites can extend entanglement distribution over long distances, but routing in such networks is challenging because satellite motion and stochastic link generation create a highly dynamic quantum topology. Existing routing methods often rely on global topology information that quickly becomes outdated due to delays in the classical control plane, while decentralized methods typically act on incomplete local information. We propose SatQNet, a reinforcement learning approach for entanglement routing in satellite-assisted quantum networks that can be decentralized at runtime. Its key innovation is an edge-centric directed line graph neural network that performs local message passing on directed edge embeddings, enabling it to better capture link properties in high-degree and time-varying topologies. By exchanging messages with neighboring repeaters, SatQNet learns a local graph representation at runtime that supports agents in establishing high-fidelity end-to-end entanglements. Trained on random graphs, SatQNet outperforms heuristic and learning-based approaches across diverse settings, including a real-world European backbone topology, and generalizes to unseen topologies without retraining.