Recent advancements in motion planning for Autonomous Vehicles (AVs) show great promise in using expert driver behaviors in non-stationary driving environments. However, learning only through expert drivers needs more generalizability to recover from domain shifts and near-failure scenarios due to the dynamic behavior of traffic participants and weather conditions. A deep Graph-based Prediction and Planning Policy Network (GP3Net) framework is proposed for non-stationary environments that encodes the interactions between traffic participants with contextual information and provides a decision for safe maneuver for AV. A spatio-temporal graph models the interactions between traffic participants for predicting the future trajectories of those participants. The predicted trajectories are utilized to generate a future occupancy map around the AV with uncertainties embedded to anticipate the evolving non-stationary driving environments. Then the contextual information and future occupancy maps are input to the policy network of the GP3Net framework and trained using Proximal Policy Optimization (PPO) algorithm. The proposed GP3Net performance is evaluated on standard CARLA benchmarking scenarios with domain shifts of traffic patterns (urban, highway, and mixed). The results show that the GP3Net outperforms previous state-of-the-art imitation learning-based planning models for different towns. Further, in unseen new weather conditions, GP3Net completes the desired route with fewer traffic infractions. Finally, the results emphasize the advantage of including the prediction module to enhance safety measures in non-stationary environments.