The flexible mobility feature of unmanned aerial vehicles (UAVs) leads to frequent handovers and serious inter-cell interference problems in UAV-assisted cellular networks. Establishing a cell-free UAV (CF-UAV) network without cell boundaries effectively alleviates frequent handovers and interference problems and has been an important topic of 6G research. However, in existing CF-UAV networks, a large amount of backhaul data increases the computational pressure on the central processing unit (CPU), which also increases system delay. Meanwhile, the mobility of UAVs also leads to time-varying channel conditions. Therefore, designing dynamic resource allocation schemes with the help of edge computing can effectively alleviate this problem. Thus, aiming at partial network breakdown in an urban-micro (UMi) environment, an urban-micro CF-UAV (UMCF-UAV) network architecture is proposed in this paper. A delay minimization problem and a dynamic task offloading (DTO) strategy that jointly optimizes access point (AP) selection and task offloading is proposed to reduce system delay in this paper. Considering the coupling of various resources and the non-convex feature of the proposed problem, a dynamic resource cooperative allocation (DRCA) algorithm based on deep reinforcement learning (DRL) to flexibly deploy AP selection and task offloading of UAVs between the edge and locally is proposed to solve the problem. Simulation results show fast convergence behavior of the proposed algorithm compared with classical reinforcement learning. Decreased system delay is obtained by the proposed algorithm compared with other baseline resource allocation schemes, with the maximize improvement being 53%.