Internet-of-Things (IoT) networks typically rely on satellite communications to provide coverage in rural areas. However, high-mobility satellite links introduce severe Doppler and delay spreads, which necessitate the use of orthogonal time frequency space (OTFS) modulation for reliable data transmission. Furthermore, the space and energy constraints on IoT devices make the perfect use case for fluid antenna systems (FAS) due to their mechanical simplicity. Hence, we propose a sophisticated FAS aided OTFS (FAS-OTFS) framework for satellite-based IoT networks. We derive analytical expressions for both the outage probability and ergodic capacity of FAS-OTFS under a general channel model, where the expressions derived are presented in integral form or as analytical bounds for efficient numerical evaluation. Additionally, we investigate a single-path fading scenario, where closed-form expressions are obtained. Our numerical results demonstrate significant performance gains in terms of both the outage probability and capacity compared to conventional OTFS systems, confirming the efficacy of FAS-OTFS in energy-constrained high-mobility environments. Our findings establish FAS-OTFS as a promising candidate for next-generation IoT communications over satellite links.