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In this work, we consider a downlink NOMA network with multiple single-antenna users and multi-antenna UAVs. In particular, the users are spatially located in several clusters by following the Poisson Cluster Process and each cluster is served by a hovering UAV with NOMA. For practical considerations, we assume that only imperfect CSI of each user is available at the UAVs. Based on this model, the problem of joint user clustering and robust beamforming design is formulated to minimize the sum transmission power, and meanwhile, guarantee the QoS requirements of users. Due to the integer variables of user clustering, coupling effects of beamformers, and infinitely many constraints caused by the imperfect CSI, the formulated problem is challenging to solve. For computational complexity reduction, the original problem is divided into user clustering subproblem and robust beamforming design subproblem. By utilizing the users' position information, we propose a k-means++ based unsupervised clustering algorithm to first deal with the user clustering problem. Then, we focus on the robust beamforming design problem. To attain insights on solving the robust beamforming design problem, we firstly investigate the problem with perfect CSI, and the associated problem is shown can be solved optimally. Secondly, for the problem in the general case with imperfect CSI, an SDR based method is proposed to produce a suboptimal solution efficiently. Moreover, we provide a sufficient condition under which the SDR based approach can guarantee to obtain an optimal rank-one solution, which is theoretically analyzed. Finally, an alternating direction method of multipliers based algorithm is proposed to allow the UAVs to perform robust beamforming design in a decentralized fashion efficiently. Simulation results demonstrate the efficacy of the proposed algorithms and transmission scheme.