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Deploying teams of unmanned aerial vehicles (UAVs) to harvest data from distributed Internet of Things (IoT) devices requires efficient trajectory planning and coordination algorithms. Multi-agent reinforcement learning (MARL) has emerged as a solution, but requires extensive and costly real-world training data. To tackle this challenge, we propose a novel model-aided federated MARL algorithm to coordinate multiple UAVs on a data harvesting mission with only limited knowledge about the environment. The proposed algorithm alternates between building an environment simulation model from real-world measurements, specifically learning the radio channel characteristics and estimating unknown IoT device positions, and federated QMIX training in the simulated environment. Each UAV agent trains a local QMIX model in its simulated environment and continuously consolidates it through federated learning with other agents, accelerating the learning process. A performance comparison with standard MARL algorithms demonstrates that our proposed model-aided FedQMIX algorithm reduces the need for real-world training experiences by around three magnitudes while attaining similar data collection performance.