Disasters are uncertain occasions that can impose a drastic impact on human life and building infrastructures. Information and Communication Technology (ICT) plays a vital role in coping with such situations by enabling and integrating multiple technological resources to develop Disaster Management Systems (DMSs). In this context, a majority of the existing DMSs use networking architectures based upon the Internet Protocol (IP) focusing on location-dependent communications. However, IP-based communications face the limitations of inefficient bandwidth utilization, high processing, data security, and excessive memory intake. To address these issues, Named Data Networking (NDN) has emerged as a promising communication paradigm, which is based on the Information-Centric Networking (ICN) architecture. An NDN is among the self-organizing communication networks that reduces the complexity of networking systems in addition to provide content security. Given this, many NDN-based DMSs have been proposed. The problem with the existing NDN-based DMS is that they use a PULL-based mechanism that ultimately results in higher delay and more energy consumption. In order to cater for time-critical scenarios, emergence-driven network engineering communication and computation models are required. In this paper, a novel DMS is proposed, i.e., Named Data Networking Disaster Management (NDN-DM), where a producer forwards a fire alert message to neighbouring consumers. This makes the nodes converge according to the disaster situation in a more efficient and secure way. Furthermore, we consider a fire scenario in a university campus and mobile nodes in the campus collaborate with each other to manage the fire situation. The proposed framework has been mathematically modeled and formally proved using timed automata-based transition systems and a real-time model checker, respectively. Additionally, the evaluation of the proposed NDM-DM has been performed using NS2. The results prove that the proposed scheme has reduced the end-to-end delay up from 2 % to 10 % and minimized up to 20 % energy consumption, as energy improved from 3 % to 20 % compared with a state-of-the-art NDN-based DMS.