Due to significant variations in the projection of the same object from different viewpoints, machine learning algorithms struggle to recognize the same object across various perspectives. In contrast, toddlers quickly learn to recognize objects from different viewpoints with almost no supervision. Recent works argue that toddlers develop this ability by mapping close-in-time visual inputs to similar representations while interacting with objects. High acuity vision is only available in the central visual field, which may explain why toddlers (much like adults) constantly move their gaze around during such interactions. It is unclear whether/how much toddlers curate their visual experience through these eye movements to support learning object representations. In this work, we explore whether a bio inspired visual learning model can harness toddlers' gaze behavior during a play session to develop view-invariant object recognition. Exploiting head-mounted eye tracking during dyadic play, we simulate toddlers' central visual field experience by cropping image regions centered on the gaze location. This visual stream feeds a time-based self-supervised learning algorithm. Our experiments demonstrate that toddlers' gaze strategy supports the learning of invariant object representations. Our analysis also reveals that the limited size of the central visual field where acuity is high is crucial for this. We further find that toddlers' visual experience elicits more robust representations compared to adults' mostly because toddlers look at objects they hold themselves for longer bouts. Overall, our work reveals how toddlers' gaze behavior supports self-supervised learning of view-invariant object recognition.