Data efficiency and robustness to task-irrelevant perturbations are long-standing challenges for deep reinforcement learning algorithms. Here we introduce a modular approach to addressing these challenges in a continuous control environment, without using hand-crafted or supervised information. Our Curious Object-Based seaRch Agent (COBRA) uses task-free intrinsically motivated exploration and unsupervised learning to build object-based models of its environment and action space. Subsequently, it can learn a variety of tasks through model-based search in very few steps and excel on structured hold-out tests of policy robustness.