Rapid three-dimensional mobility in flying ad hoc networks (FANETs) causes routes selected from the current topology to become invalid before packets reach subsequent hops, particularly for flows with strict deadlines. Existing approaches commonly rely on point-wise position prediction, optimize average delay, and provide limited treatment of predictive uncertainty. This paper proposes a mobilitypredictive routing framework based on a time-expanded future contact graph and a physics-informed temporal graph neural network with kinematic regularization. The model predicts multi-horizon link-survival probabilities, residual link lifetimes, delay quantiles, and uncertainty, which are calibrated and propagated into an explicit deadline-constrained route-selection process. The framework is evaluated under multiple three-dimensional mobility models, unseen mobility conditions, noisy and delayed telemetry, and different network scales against conventional, predictive, and GNN- based
routing methods. At 25 m/s, the proposed method achieves a deadline satisfaction ratio of 0.883±0.011. Under unseen mobility with 300-ms telemetry delay, it reduces route breaks
by 36.3% relative to the uncalibrated temporal GNN. At 20 packets/s, it lowers the 95th-percentile delay by 18.6% over the strongest practical baseline, while requiring 103±4.1
signaling bytes per delivered packet and 12.1±0.8 ms inference latency for 100 UAVs