The ability to inhibit saccades toward suddenly appearing peripheral stimuli (prosaccades) and direct them to contralateral locations instead (antisaccades) is a crucial marker of eye movement control. Typically developing infants as young as 4-month-olds can learn to inhibit reflexive saccades to peripheral stimuli, but they do not produce antisaccades, whose development later in infancy and its underlying neural computations remain unexplored. Here we tested oculomotor control in typically developing toddlers and toddlers with fragile X syndrome (FXS), a disorder of known genetic origin that allows the investigation of the neuro-computational properties contributing to the development of saccadic control. Typically developing toddlers decreased looking toward peripheral cues that predicted contralateral rewards, whose appearance they anticipated. Furthermore, this correlated with age, indicating a gradual development of saccadic control. In contrast with the typical case, toddlers with FXS did not decrease their looks to peripheral onsets that predicted contralateral events. Importantly, the atypical pattern of performance was also evident in the elimination of the correlation with mental or chronological age found in controls. Taken together, the findings suggest that control of saccades and its developmental trajectory is atypical in toddlers with FXS, consistent with inhibitory deficits previously shown at later ages in this condition. Potential implications for the neural mechanisms underlying the typical and atypical development of oculomotor control are discussed.