Deep reinforcement learning-based quadrupedal jumping robots have emerged as promising solutions for extraterrestrial exploration missions, particularly in lunar surface operations. However, a critical challenge persists in addressing uncertain environments characterized by stochastic and irregular terrain features. This study proposes an enhanced Soft Actor-Critic framework incorporating a state-dependent Policy Feature-Related noise injection to address the adaptability limitations of quadrupedal robots in unstructured lunar terrains. In contrast to conventional independent Gaussian noise methods, the proposed approach establishes a functional mapping between strategic decision-making features, which are derived from the policy network and naturally connected to input states, and the exploration noise generation process. This generates structured exploration signals that maintain the necessary stochasticity while ensuring temporal coherence. Simulation experiments validate the training effects of the proposed method and demonstrate its ability to meet the requirements of jumping stabilization under lunar gravitational conditions and autonomous adaptation of limb coordination strategies for stochastic terrain.