Autism Spectrum Disorder is a neurodevelopmental trouble for which no objective biomarker has yet been discovered. The search for an accessible biomarker aims, in particular, for early autism screening, in order to optimize tailored intervention when necessary. In this context, eye-tracking has been now used for numerous years in the field of research on autism as it allows for non-intrusive, no-contact recordings even in very young children. However, individual oculometric parameters, while showing significant differences between groups of autistic and non-autistic individuals, are not discriminative enough for individual screening. In this study, we combined oculometric measures with pupillary parameters obtained simultaneously by the eye-tracker, and used a machine-learning approach to estimate the discriminative performance of such combinations of parameters. Data were obtained in 72 autistic and 93 neurotypical 2-13 years old children observing objects and faces during less than a minute. We used the Weka datamining software, testing 36 machine-learning algorithms without any a priori, in order to describe robust and convergent performance. Moreover, we chose to report only performance associated with high sensitivity, specificity and accuracy. We showed that oculo-pupillometric combinations of parameters allowed to reach outstanding discriminative performance in young children, paving the way for a clinical use.