Conversational agents are increasingly being explored to support healthcare delivery, particularly in resource-constrained settings such as rural Nepal. Large-scale conversational models typically rely on internet connectivity and cloud infrastructure, which may not be accessible in rural areas. In this study, we fine-tuned DialoGPT, a lightweight generative dialogue model that can operate offline, on a synthetically constructed dataset of doctor-patient interactions covering ten common diseases prevalent in rural Nepal, including common cold, seasonal fever, diarrhea, typhoid fever, gastritis, food poisoning, malaria, dengue fever, tuberculosis, and pneumonia. Despite being trained on a limited, domain-specific dataset, the fine-tuned model produced coherent, contextually relevant, and medically appropriate responses, demonstrating an understanding of symptoms, disease context, and empathetic communication. These results highlight the adaptability of compact, offline-capable dialogue models and the effectiveness of targeted datasets for domain adaptation in low-resource healthcare environments, offering promising directions for future rural medical conversational AI.