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A growing number of service providers are exploring methods to improve server utilization and reduce power consumption by co-scheduling high-priority latency-critical workloads with best-effort workloads. This practice requires strict resource allocation between workloads to reduce contention and maintain Quality-of-Service (QoS) guarantees. Prior work demonstrated promising opportunities to dynamically allocate resources based on workload demand, but may fail to meet QoS objectives in more stringent operating environments due to the presence of resource allocation cliffs, transient fluctuations in workload performance, and rapidly changing resource demand. We therefore propose PROMPT, a novel resource allocation framework using proactive QoS prediction to guide a reinforcement learning controller. PROMPT enables more precise resource optimization, more consistent handling of transient behaviors, and more robust generalization when co-scheduling new best-effort workloads not encountered during policy training. Evaluation shows that the proposed method incurs 4.2x fewer QoS violations, reduces severity of QoS violations by 12.7x, improves best-effort workload performance, and improves overall power efficiency over prior work.