This study presents an innovative approach to optimal gait control for a soft quadruped robot enabled by four Compressible Tendon-driven Soft Actuators (CTSAs). Improving our previous studies of using model-free reinforcement learning for gait control, we employ model-based reinforcement learning (MBRL) to further enhance the performance of the gait controller. Compared to rigid robots, the proposed soft quadruped robot has better safety, less weight, and a simpler mechanism for fabrication and control. However, the primary challenge lies in developing sophisticated control algorithms to attain optimal gait control for fast and stable locomotion. The research employs a multi-stage methodology, including state space restriction, data-driven model training, and reinforcement learning algorithm development. Compared to benchmark methods, the proposed MBRL algorithm, combined with post-training, significantly improves the efficiency and performance of gait control policies. The developed policy is both robust and adaptable to the robot's deformable morphology. The study concludes by highlighting the practical applicability of these findings in real-world scenarios.