Asymmetric patterns of frontal brain electrical activity reflect approach and avoidance tendencies, with stability of relative right activation associated with withdrawal emotions/motivation and left hemisphere activation linked with approach and positive affect. However, considerable shifts in approach/avoidance-related lateralization have been reported for children not targeted because of extreme temperament. In this study, dynamic effects of frontal electroencephalogram (EEG) power within and across hemispheres were examined throughout early childhood. Specifically, EEG indicators at 5, 10, 24, 36, 48, and 72 months-of-age (n = 410) were analyzed via a hybrid of difference score and panel design models, with baseline measures and subsequent time-to-time differences modeled as potentially influencing all subsequent amounts of time-to-time change (i.e., predictively saturated). Infant sex was considered as a moderator of dynamic developmental effects, with temperament attributes measured at 5 months examined as predictors of EEG hemisphere development. Overall, change in left and right frontal EEG power predicted declining subsequent change in the same hemisphere, with effects on the opposing neurobehavioral system enhancing later growth. Infant sex moderated the pattern of within and across-hemisphere effects, wherein for girls more prominent left hemisphere influences on the right hemisphere EEG changes were noted and right hemisphere effects were more salient for boys. Largely similar patterns of temperament prediction were observed for the left and the right EEG power changes, with limited sex differences in links between temperament and growth parameters. Results were interpreted in the context of comparable analyses using parietal power values, which provided evidence for unique frontal effects.