Autism spectrum disorder (ASD) is a lifelong neurodevelopmental disorder with very high prevalence around the world. Research progress in the field of ASD facial analysis in pediatric patients has been hindered due to a lack of well-established baselines. In this paper, we propose the use of the Vision Transformer (ViT) for the computational analysis of pediatric ASD. The presented model, known as ViTASD, distills knowledge from large facial expression datasets and offers model structure transferability. Specifically, ViTASD employs a vanilla ViT to extract features from patients' face images and adopts a lightweight decoder with a Gaussian Process layer to enhance the robustness for ASD analysis. Extensive experiments conducted on standard ASD facial analysis benchmarks show that our method outperforms all of the representative approaches in ASD facial analysis, while the ViTASD-L achieves a new state-of-the-art.