This paper studies an unmanned aerial vehicle (UAV)-enabled wireless power communication networks (WPCN-s), where the UAV provides energy for mobile user nodes (M-UNs) and receives information from M-UNs. The movement of M-UN complies with a Gauss-Markov random model. To ensure acceptable quality-of-service (QoS), we consider dynamically planning the flight path of the UAV according to the movements of M-UNs. Since the flight time of UAV is restricted by limited energy, nonorthogonal multiple access (NOMA) is adopted to access a large number of M-UNs for simultaneous information transmission. Based on the above considerations, we aim to maximize the throughput via path planning of the UAV, subject to the QoS requirements of M-UNs and the UAV's energy constraint. To handle the challenges brought by dynamically changing channels to solving the problem, we propose a QoS-based double deep Q-learning network (DDQN). Numerical simulation results show that, compared with the conventional algorithms, the proposed framework achieves higher throughput.