The convergence of Quantum Computing (QC) and Artificial Intelligence (AI) is reshaping computational paradigms, creating the need for a new class of system software capable of managing hybrid workloads. This paper presents Q-OS, a Quantum-Aware Operating System designed to orchestrate hybrid quantum-classical AI pipelines across cloud and edge environments. Q-OS introduces three novel system components: a Quantum Scheduling Kernel that intelligently allocates portions of AI workloads (such as optimization or sampling) to quantum co-processors; a Quantum Resource Virtualization Layer that abstracts quantum devices as logical accelerators; and a Quantum-AI Compiler Interface that dynamically maps AI operations from frameworks such as TensorFlow and PyTorch into executable quantum kernels. Experimental evaluations using hybrid workloads-including large language model inference (The Pile dataset), quantum-classical generative adversarial networks (CelebA dataset), and reinforcement learning control (OpenAI Gym)-demonstrate that Q-OS achieves up to 32% reduction in end-to-end latency and 27% improvement in energy efficiency compared to classical distributed systems. The results indicate that Q-OS establishes a scalable foundation for the next generation of intelligent computing infrastructures, bridging quantum and AI ecosystems for real-world deployment.