Neonatal brain MRI is a resolution-critical task due to the small brain of neonates. Among post-acquisition resolution-enhancement techniques, deep learning has shown promising results. Most state-of-the-art deep learning-based super-resolution methods work on 2D slices, so ignore the 3D nature of the brain anatomy. Learning on 3D images requires large-scale training datasets of high-resolution volumes that are, unfortunately, difficult to acquire. We developed a methodology that enables learning 3D gradient structures from 2D slices for an individual subject without the need for large, auxiliary high-resolution datasets. Experiments on clinical data from ten neonates demonstrate our approach outperformed state-of-the-art MRI super-resolution methods.