Small datasets form a significant portion of releasable data in high sensitivity domains such as healthcare. But, providing differential privacy for small dataset release is a hard task, where current state-of-the-art methods suffer from severe utility loss. As a solution, we propose DPRP (Differentially Private Data Release via Random Projections), a reconstruction based approach for releasing differentially private small datasets. DPRP has several key advantages over the state-of-the-art. Using seven diverse real-life datasets, we show that DPRP outperforms the current state-of-the-art on a variety of tasks, under varying conditions, and for all privacy budgets.