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It is critical but challenging to provide efficient information services to support disaster-response operations in disaster-hit areas. A UAVFog-assisted data-driven disaster-response architecture, which combines unmanned aerial vehicles (UAVs) and fog computing paradigm, showed many advantages in response latency and on-the-fly deployment. This paper aims to jointly optimize the deployment of service functions (SFs) and the task scheduling at UAVFog nodes to minimize the task response latency. After introducing the collaboration structure between UAVFog nodes, joint SF deployment and task scheduling is formulated as an optimization problem. Then, three algorithms are put forward to tackle the problem: 1) Dependency and topology-aware SF deployment (DeToSFD) algorithm is developed to determine the initial deployment location of each SF; 2) Context-aware greedy task scheduling (CoGTS) algorithm is put forward to schedule an arrived task; 3) Congestion-aware SF reallocation (CoSFR) algorithm is developed to reallocate SFs in case of congestion at an instance of an SF. Finally, a series of experiments are conducted to evaluate the performance of the proposed algorithms. Experimental results show that DeToSFD, CoGTS, and CoSFR could greatly reduce the task response latency of the UAVFog system in diverse parameter settings. [ABSTRACT FROM AUTHOR]