Energy remains one of the most critical constraints for autonomous planetary rovers, shaping their scientific output, operational safety, and long-term mission performance. Current Mars missions often treat task scheduling and energy prediction as separate processes, which leads to conservative planning, limited autonomy, and avoidable replanning from Earth. This work addresses this gap by developing an integrated framework that links task prioritization with physics-informed energy prediction for space-like rovers. Building on limitations in existing mission planning systems such as MAPGEN and ASPEN, this study introduces an Energy-Aware Hierarchical Task Network with Timeline Scheduling (E-HTN-T). The approach embeds a simplified traction-based energy model directly into the planning loop and evaluates task feasibility using a minimum-energy reserve constraint. Unlike traditional schedulers that treat energy as static, the proposed method incorporates the influence of terrain, subsystem power consumption, and background power generation, enabling more realistic decision-making under uncertainty. Seven representative operational scenarios inspired by Mars rover workflows were constructed to evaluate the method. These include routine navigation, scientific task execution, varied terrain conditions, and degraded power availability. Across all scenarios, the integrated planner consistently produced safer and more complete task schedules compared to baseline strategies. Results show that linking energy prediction to task selection reduces infeasible plans and increases completed scientific objectives, demonstrating robustness under terrain variability and low-battery conditions. This research demonstrates the potential of physics-aware scheduling to enhance autonomous rover operations by reducing energy-related failures and enabling more efficient use of mission time. The framework provides a foundation for future planners that integrate structural mechanics, terramechanics, and autonomous decision-making to support next-generation planetary missions.