This research presents a comprehensive analysis of the dynamic behavior of bidirectional functionally graded (BDFG) Reissner-Mindlin plates subjected to moving loads, with a particular focus on material gradation effects and structural optimization. The study assumes a symmetric bidirectional variation of material properties along both the length and thickness directions, governed by a nonlinear power-law distribution. By strategically tailoring this material gradation, significant improvements in structural performance and dynamic stability are achieved. A finite element model is meticulously developed and rigorously validated against established benchmarks to ensure accuracy in predicting the mechanical response under varying boundary conditions and moving load velocities. The results highlight that symmetric bidirectional material gradation plays a critical role in enhancing vibration resistance, reducing deflections, and improving overall mechanical performance. Surprisingly, contrary to conventional assumptions, increasing material gradation nonlinearity does not always yield enhanced dynamic stability, instead, certain configurations exhibit unexpected resonance phenomena at specific velocity thresholds, challenging traditional design paradigms. Additionally, the study uncovers a counterintuitive dependency of dynamic responses on boundary conditions, where certain soft-clamped configurations outperform fully clamped ones in mitigating peak deflections under high-speed loads. These findings offer novel design insights for optimizing advanced structural components across multiple engineering applications, including civil, mechanical, and aerospace structures, where high-performance functionally graded materials (FGMs) are crucial for sustaining dynamic loads efficiently.