Large Language Models (LLMs) demonstrate strong generalization and reasoning abilities, making them well-suited for complex decision-making tasks such as medical consultation (MC). However, existing LLM-based methods often fail to capture the dual nature of MC, which entails two distinct sub-tasks: symptom inquiry, a sequential decision-making process, and disease diagnosis, a classification problem. This mismatch often results in ineffective symptom inquiry and unreliable disease diagnosis. To address this, we propose textbfDDO, a novel LLM-based framework that performs textbfDual-textbfDecision textbfOptimization by decoupling and independently optimizing the the two sub-tasks through a collaborative multi-agent workflow. Experiments on three real-world MC datasets show that DDO consistently outperforms existing LLM-based approaches and achieves competitive performance with state-of-the-art generation-based methods, demonstrating its effectiveness in the MC task.