(1) Background: Children with autism spectrum disorder (ASD) show certain characteristics in visual attention which generate difficulties in the integration of relevant social information to set the basis of communication. Gaze following and pupil dilation could be used to identify signs for the early detection of ASD. Eye-tracking methodology allows objective measurement of these anomalies in visual attention. The aim is to determine whether measurements of gaze following and pupillary dilation in a linguistic interaction task, captured using eye-tracking methodology, are objective for early diagnosis of ASD. (2) Methods: 20 children between 17 and 24 months of age, made up of 10 neurotypical children and 10 children with ASD were paired together according to chronological age. A human face on a monitor pronounced pseudowords associated with pseudo-objects. Gaze following and pupil dilation was registered during the task. (3) Results: Significant statistical differences were found in the time of gaze fixation on the human face and on the object, as well as in the number of gazes. Also, there were significant differences in the maximum peak of pupil dilation, this being found in the neurotypical group at the moment of processing of the pseudoword, and in the ASD group in the baseline prior to the task (4) Conclusions: The registration and the duration of gaze, and the measurement of pupil dilation with ‘eye-tracker’ are objective measures for early detection of ASD.