Understanding how children's spontaneous language behavior relates to standardized metrics of language development remains a crucial challenge in developmental science, particularly given the time and resources required for many traditional lab-based assessments. This study investigates whether automated analysis of naturalistic, child-centered audio recordings can index the developmental trajectory of speech-language abilities. Using a longitudinal design following N=130 preschoolers, we employed deep learning methods to compute Canonical Proportion - a theoretically-motivated metric that reflects both speech motor control development and phonological representation building - from naturalistic, child-centered audio recordings at age 3 years. Canonical proportion measures significantly predicted multiple dimensions of speech-language development longitudinally, formally assessed in the lab one year later at age 4. The strongest relationships were found for consonant articulation skill and vocabulary size, suggesting that early speech production patterns may moderately index numerous later facets of language development. These findings outline a potential relationship between children's spontaneous, everyday language behavior and more traditional language development metrics, while demonstrating the potential for automated measures to expand and diversify research in developmental science.