The Internet of Things (IoT) brings connectivity to a massive number of devices that demand energy-efficient solutions to deal with limited battery capacities, uplink-dominant traffic, and channel impairments. In this work, we explore the use of Unmanned Aerial Vehicles (UAVs) equipped with configurable antennas as a flexible solution for serving low-power IoT networks. We formulate an optimization problem to set the position and antenna beamwidth of the UAV, and the transmit power of the IoT devices subject to average-Signal-to-average-Interference-plus-Noise Ratio Quality of Service (QoS) constraints. We minimize the worst-case average energy consumption of the latter, thus, targeting the fairest allocation of the energy resources. The problem is non-convex and highly non-linear; therefore, we re-formulate it as a series of three geometric programs that can be solved iteratively. Results reveal the benefits of planning the network compared to a random deployment in terms of reducing the worst-case average energy consumption. Furthermore, we show that the target average-Signal-to-average-Interference-plus-Noise Ratio is limited by the number of IoT devices, and highlight the dominant impact of the UAV hovering height when serving wider areas. Our proposed algorithm outperforms other optimization benchmarks in terms of minimizing the average energy consumption at the most energy-demanding IoT device, and convergence time.