In this paper, a dialogue system for Hospital domain in Telugu, which is a resource-poor Dravidian language, has been built. It handles various hospital and doctor related queries. The main aim of this paper is to present an approach for modelling a dialogue system in a resource-poor language by combining linguistic and domain knowledge. Focusing on the question answering aspect of the dialogue system, we identified Question Classification and Query Processing as the two most important parts of the dialogue system. Our method combines deep learning techniques for question classification and computational rule-based analysis for query processing. Human evaluation of the system has been performed as there is no automated evaluation tool for dialogue systems in Telugu. Our system achieves a high overall rating along with a significantly accurate context-capturing method as shown in the results.