Low-field magnetic resonance imaging (MRI) offers affordable access to diagnostic imaging but faces challenges such as prolonged acquisition times and reduced image quality. Although accelerated imaging via k-space undersampling helps reduce scan time, image quality enhancement methods often rely on spatial-domain postprocessing. Deep learning achieved state-of-the-art results in both domains. However, most models are trained and evaluated using in-distribution (InD) data, creating a significant gap in understanding model performance when tested using out-of-distribution (OOD) data. To address these issues, we propose a novel framework that reconstructs high-field-like MR images directly from undersampled low-field MRI k-space, quantifies the impact of reduced sampling, and evaluates the generalisability of the model using OOD. Our approach utilises a k-space dual channel U-Net to jointly process the real and imaginary components of undersampled k-space, restoring missing frequency content, and incorporates an ensemble strategy to generate uncertainty maps. Experiments on low-field brain MRI demonstrate that our k-space-driven image quality enhancement outperforms the counterpart spatial-domain and other state-of-the-art baselines, achieving image quality comparable to full high-field k-space acquisitions using OOD data. To the best of our knowledge, this work is among the first to combine low-field MR image reconstruction, quality enhancement using undersampled k-space, and uncertainty quantification within a unified framework.