The automatic detection of gaze targets in autistic children through artificial intelligence can be impactful, especially for those who lack access to a sufficient number of professionals to improve their quality of life. This paper introduces a new, real-world AI application for gaze target detection in autistic children, which predicts a child's point of gaze from an activity image. This task is foundational for building automated systems that can measure joint attention-a core challenge in Autism Spectrum Disorder (ASD). To facilitate the study of this challenging application, we collected the first-ever Autism Gaze Target (AGT) dataset. We further propose a novel Socially Aware Coarse-to-Fine (SACF) gaze detection framework that explicitly leverages the social context of a scene to overcome the class imbalance common in autism datasets-a consequence of autistic children's tendency to show reduced gaze to faces. It utilizes a two-pathway architecture with expert models specialized in social and non-social gaze, guided by a context-awareness gate module. The results of our comprehensive experiments demonstrate that our framework achieves new state-of-the-art performance for gaze target detection in this population, significantly outperforming existing methods, especially on the critical minority class of face-directed gaze.