Prior work on 6-DoF object pose estimation has largely focused on instance-level processing, in which a textured CAD model is available for each object being detected. Category-level 6-DoF pose estimation represents an important step toward developing robotic vision systems that operate in unstructured, real-world scenarios. In this work, we propose a single-stage, keypoint-based approach for category-level object pose estimation that operates on unknown object instances within a known category using a single RGB image as input. The proposed network performs 2D object detection, detects 2D keypoints, estimates 6-DoF pose, and regresses relative bounding cuboid dimensions. These quantities are estimated in a sequential fashion, leveraging the recent idea of convGRU for propagating information from easier tasks to those that are more difficult. We favor simplicity in our design choices: generic cuboid vertex coordinates, single-stage network, and monocular RGB input. We conduct extensive experiments on the challenging Objectron benchmark, outperforming state-of-the-art methods on the 3D IoU metric (27.6% higher than the MobilePose single-stage approach and 7.1% higher than the related two-stage approach).