Drones or Unmanned aerial vehicles have had a profound effect on how we perceive and interact with the world. These remotely piloted or autonomous aircraft have surpassed their military origins and found diverse applications in fields such as agriculture, infrastructure inspection, disaster management, delivery services, and recreational activities. Their ability to swiftly navigate the skies, capture high resolution aerial images, and execute precise tasks has made them indispensable tools in time critical applications like disaster monitoring and search-and-rescue missions. However, their increased usage has raised concerns regarding security issues including unauthorized access, data breaches, cyber-attacks, and physical threats. The UAV network being highly dynamic, the adversaries may exploit drone failures to intrude into the network and pose serious data breaches. It is, therefore, essential to employ robust security measures, such as authentication, encryption, physical security measures, and proactive monitoring, to mitigate the risks associated with drone operations. However, limited resource constraints can make it challenging to implement heavy encryption and cryptographic algorithms on drones. In this paper, we have proposed a lightweight mutual authentication and key agreement protocol for disaster management applications, incorporating physically unclonable technology to secure communication. Additionally, the protocol is enhanced to manage security risks during UAV failures. The protocol has been validated using the Scyther simulation tool, and an informal security analysis has been presented to verify that all security requirements have been met. Additionally, the performance of the protocol has been compared with state-of-the-art approaches by calculating the network latency in terms of computational and communication costs. The analysis shows that the protocol is effective and practical in time-bound scenarios.