Stereo-based 3D obstacle perception for autonomous driving is currently constrained by an imbalanced triplet: deployment cost, detection accuracy, and open-set adaptability. While existing methods struggle to balance these three competing objectives, there is an urgent demand for high-precision, real-time algorithms capable of detecting arbitrary obstacles in the wild. In this paper, we present DDStereo, a novel Dual-Decoder Stereo Transformer that achieves a synergistic integration of 3D object detection and Out-of-Distribution (OoD) road anomaly detection. Leveraging the geometric priors of stereo disparity, our approach effectively couples 3D attribute regression with open-set foreground detection within a streamlined dual-branch decoder architecture. Conventional methods rely on complex feature-level fusion; DDStereo maintains execution efficiency by employing a decoupled decoding strategy and shared object-level queries to ensure cross-modal target alignment. Extensive evaluations of public benchmarks demonstrate that DDStereo not only achieves state-of-the-art accuracy under open-set and closed-set protocols. Our method delivers real-time performance comparable to monocular 3D detection baselines, providing a cost-effective solution for the perception of obstacles of the normal and OoD category. Code and models are available at https://github.com/shiyi-mu/DDStereo.