Children rapidly learn to use language to effect a variety of communicative acts, such as proposing actions, asking questions, and making promises. While prior work has characterized this development in cross-sectional corpora, these analyses have been unable to comprehensively track individual differences in children's acquisition of communicative acts. We analyzed a longitudinal corpus of parent-child interactions from ages 14 to 58 months. We find that children's repertoires of communicative acts diversify over this period, with stable individual differences in the diversity of children's communicative act repertoires. Further, the diversities of parents' and children's communicative act repertoires are correlated. Children with more diverse communicative act repertoires also have larger vocabularies and use more diverse syntactic frames, suggesting links between discourse development and lexical and syntactic knowledge. Taken together, this work provides new insight into individual trajectories of communicative development and connections between communicative act use and other levels of language structure.