The proliferation of Internet of Things (IoT) networks has created an urgent need for sustainable energy solutions, particularly for the battery-constrained spatially distributed IoT nodes. While low-altitude uncrewed aerial vehicles (UAVs) employed with wireless power transfer (WPT) capabilities offer a promising solution, the line-of-sight channels that facilitate efficient energy delivery also expose sensitive operational data to adversaries. This paper proposes a novel low-altitude UAV-carried movable antenna-enhanced transmission system joint WPT and covert communications, which simultaneously performs energy supplements to IoT nodes and establishes transmission links with a covert user by leveraging wireless energy signals as a natural cover. Then, we formulate a multi-objective optimization problem that jointly maximizes the total harvested energy of IoT nodes and sum achievable rate of the covert user, while minimizing the propulsion energy consumption of the low-altitude UAV. To address the non-convex and temporally coupled optimization problem, we propose a mixture-of-experts-augmented soft actor-critic (MoE-SAC) algorithm that employs a sparse Top-K gated mixture-of-shallow-experts architecture to represent multimodal policy distributions arising from the conflicting optimization objectives. We also incorporate an action projection module that explicitly enforces per-time-slot power budget constraints and antenna position constraints. Simulation results demonstrate that the proposed approach significantly outperforms some baseline approaches and other state-of-the-art deep reinforcement learning algorithms.