This study measured changes in switches of attention between 1 and 9 months of age in 67 typically developing infants. Remote eye-tracking (Tobii X120) was used to measure saccadic latencies, related to switches of fixation, as a measure of shifts of attention, from a central stimulus to a peripheral visual target, measured in the Fixation Shift Paradigm. Fixation shifts occur later if the central fixation stimulus stays visible when the peripheral target appears (competition condition), than if the central stimulus disappears as the peripheral target appears (non-competition condition). This difference decreases with age. Our results show significantly faster disengagement in infants over 4 months than in the younger group, and provide more precise measures of fixation shifts, than behavioural observation with the same paradigm. Reduced saccadic latencies in the course of a test session indicate a novel learning effect. The Fixation Shift Paradigm combined with remote eye-tracking measures showed improved temporal and spatial accuracy compared to direct observation by a trained observer, and allowed an increased number of trials in a short testing time. This makes it an infant-friendly non-invasive procedure, involving minimal observational training, suitable for use in future studies of clinical populations to detect early attentional abnormalities in the first few months of life.