The route planning of time-sensitive air-cargo is becoming more important with the growing air-network congestion and delays. We consider a freight forwarder's routing of a time-sensitive air-cargo in the presence of real-time and historical information regarding flight availability, departure delays and travel times. A departure delay estimation model is developed to account for real-time information inaccuracy. A novel Markov decision model is formulated and solved with online backward induction. Through synthetic experiments and case studies, we demonstrate that dynamic routing with real-time information can improve delivery reliability and reduce expected cost.