Digital Twin is an emerging technology with potentials to reshape the future of industries and societies. Physical and digital systems are interconnected with real-time data transfer. One of the important benefits of digital twins is remote monitoring. For reliable and efficient monitoring, a high-fidelity digital twin should be implemented where continuous synchronization between physical entities and digital counter parts is to be done. In this study, we consider a scenario where a digital twin is developed to monitor a post-disaster area. To build a high-fidelity digital twin, an unmanned aerial vehicle is deployed to help in gathering real-time information from sensors, process them, and send continuous status updates to the base station where information freshness is critical so that rapid service of affected areas can be provided. We optimize digital twin accuracy, UAV trajectory and information freshness to guarantee optimized rescue response by formulating and solving a non-convex optimization problem. We conduct extensive simulations and demonstrate the effectiveness of our proposed approach, which proves to be superior over two base line approaches. This provides value-added services in various contexts through remote real-time monitoring, intelligent operation and maintenance and adaptive optimization of assets.