Developing robust Natural Language Understanding (NLU) for morphologically rich Dravidian languages like Kannada, Malayalam, Tamil, and Telugu presents significant challenges due to their agglutinative nature and syntactic complexity. In this work, we present the Dravidian NLP Suite tackling five core tasks: Morphological Analysis (MA), POS Tagging (POS), Named Entity Recognition (NER), Dependency Parsing (DEP), and Coreference Resolution (CR), trained for monolingual models and multilingual models. To facilitate this, we present the Dravida dataset, meticulously annotated multilingual corpus for these tasks across all four languages. Our experiments demonstrate that a multilingual model, which utilizes shared linguistic features and cross-lingual patterns inherent to the Dravidian family, consistently outperforms its monolingual counterparts across all tasks. These findings suggest that multilingual learning is an effective approach for enhancing Natural Language Understanding (NLU) capabilities, particularly for languages belonging to the same family. To the best of our knowledge, this is the first work to jointly address all these core tasks on the Dravidian languages.