In the aftermath of disasters, where the communication infrastructure is often impaired or completely unavailable, unmanned aerial vehicle (UAV) assisted Mobile Ad Hoc network(MANET) is a promising choice to recover wireless communication. However, affected by the dynamic topology and time-varying channel quality caused by the nodes' mobility in emergency scenarios, it is difficult to guarantee the quality of service (QoS) of various types of packets in terms of transmission delay. In this paper, a dynamic priority packet scheduling scheme is proposed to maintain high QoS in post-disaster UAV assisted MANET, where not only the occurred packet delay has experienced but also the impact that will occur in the future transmission is taken into consideration on the priority assignment. Specifically, to characterize the dynamic features of nodes, the Gauss-Markov Mobility Model is exploited. Then to incorporate the impacts of the node's movement, as well as the instability of the topology and the time-varying channel quality into the packet's priority assignment, we estimate the packet's transmission delay where the device-to-device(D2D), device-to- UAV(D2U), and UAV-to-UAV(U2U) channels are all specified, and theoretically analyzed the probability of link duration in the future transmission. Simulation results show that the proposed dynamic priority scheme outperforms the static priority and (first in first out) FIFO scheme in terms of the overall packets transmission success ratio and transmission delay.