Quantum machine learning integrates quantum features such as superposition and entanglement into learning processes, offering the potential to outperform classical methods in certain tasks. Among these approaches, quantum reservoir computing (QRC) has attracted considerable attention due to its simple structure and strong performance. However, existing QRC models remain limited in high-dimensional nonlinear representation and scalability, thereby constraining their computational performance in practical applications. In this work, we propose a quantum reservoir architecture that employs hyperentangled states to expand the effective dimensionality of the reservoir, enabling high-dimensional quantum information to be encoded within a small number of physical carriers. Based on this architecture, we design an optical scheme that serves as a physically realizable reservoir layer for QRC. Numerical simulations on high-dimensional nonlinear regression tasks, including the nonlinear autoregressive moving average of order 30 and Mackey-Glass tasks, demonstrate that the proposed architecture achieves high prediction accuracy and strong nonlinear mapping capability, thus paving a way toward scalable, high-dimensional, and efficient QRC.