Early language acquisition is vital for child cognitive and social development. Timely identification of language delays enables effective interventions. Traditional Language Sample Analysis (LSA) methods, the gold standard for assessing language acquisition, are time-consuming, making automation a promising alternative. Yet, analyzing spontaneous speech for linguistic features is hard due to errors from spoken language processing (SLP) systems. This study uses the KidsTALC dataset to explore the link between SLP performance and LSA measures of early language acquisition. We use a child-adapted ASR model to assess LSA measures, focusing on lexical diversity, on both human and machine transcripts. Our findings show that some LSA measures, like HD-D and vocd-D, are robust to imperfect ASR, with correlations over 0.9. This suggests that ASR-driven LSA, with proper methods and metric selection, can offer valuable insights for early language evaluation and aid in therapy decisions.