This paper studies a multi-user multiple-input-single-output (MU-MISO) Internet of Things (IoT) network powered by wireless power transfer (WPT). The network consists of one hybrid data-and-energy access point (HAP) having multiple antennas and several single-antenna IoT nodes. The HAP coordinates energy/information transfer to/from the nodes in the downlink (DL)/uplink (UL) using frequency-division duplexing (FDD). On the one hand, in order for WPT to effectively harness the potential of multiple antennas, it requires such techniques as energy beamforming (EB). On the other hand, efficient EB can only be achieved if channel state information (CSI) is available to the transmitter, which, in FDD systems, can be accomplished through UL feedback. Therefore, the UL channel frames are split into two phases in our scheme: the CSI feedback phase during which the IoT nodes feed CSI back to the HAP, and the WIT phase where the HAP performs wireless information transmission (WIT). To ensure rate fairness among the IoT nodes, we maximize the minimum expected WIT data rate among the nodes. This problem is non-convex and thus difficult to solve optimally. To tackle this challenge, we decouple the original optimization problem into tractable sub-problems and solve them in an alternative manner. Finally, we analyze the behavior of this system when the number of HAP antennas increases. Simulation results corroborate the accuracy of our analysis.