Superresolution T2-weighted fetal-brain magnetic-resonance imaging (FBMRI) traditionally relies on the availability of several orthogonal low-resolution series of 2-dimensional thick slices (volumes). In practice, only a few low-resolution volumes are acquired. Thus, optimization-based image-reconstruction methods require strong regularization using hand-crafted regularizers (e.g., TV). Yet, due to in utero fetal motion and the rapidly changing fetal brain anatomy, the acquisition of the high-resolution images that are required to train supervised learning methods is difficult. In this paper, we sidestep this difficulty by providing a proof of concept of a self-supervised single-volume superresolution framework for T2-weighted FBMRI (SAIR). We validate SAIR quantitatively in a motion-free simulated environment. Our results for different noise levels and resolution ratios suggest that SAIR is comparable to multiple-volume superresolution reconstruction methods. We also evaluate SAIR qualitatively on clinical FBMRI data. The results suggest SAIR could be incorporated into current reconstruction pipelines.