Quadruped robots exhibit excellent mobility and terrain adaptability, making them widely used in complex mission scenarios. However, during operations on unstructured terrains, vibrations caused by foot-terrain impacts and significant disturbances induced by uneven ground can destabilize the payload, severely affecting mission performance. To address this issue, this paper introduces a six-degree-of-freedom parallel stabilization platform into the payload stabilization system mounted on the back of quadruped robots, establishing an active disturbance compensation system independent from the robot's main controller. A kinematic model of the parallel stabilization platform is developed, and a closed-loop attitude control framework suitable for this integrated system is designed and implemented, enabling decoupled control between robot joint angles and the stabilization platform. A physical prototype has been built and tested under various conditions, including slow robot posture changes, rough terrain traversal, gentle slope navigation, and stair climbing, collecting experimental data across different operating scenarios. The system's ability to track given signals was further evaluated to validate its attitude control performance. Experimental results demonstrate that the proposed integrated system effectively suppresses low-frequency, large-amplitude disturbances caused by terrain irregularities, provides notable suppression of high-frequency vibrations generated by gait dynamics, and achieves superior attitude tracking performance, thereby expanding the practical application scope of quadruped robots.