Vocabulary growth and syntactic development are known tobe highly correlated in early child language. What determineswhen words are acquired and how can this help us understandwhat drives early language development? We train an LSTMlanguage model, known to detect syntactic regularities that arerelevant for predicting the difficulty of words, on child-directedspeech. We use the average surprisal of words for the model,which encodes sequential predictability, as a predictor for theage of acquisition of words in early child language. We com-pare this predictor to word frequency and others and find thataverage surprisal is a good predictor for the age of acquisitionof function words and predicates beyond frequency, but notfor nouns. Our approach provides insight into what makes agood model of early word learning, especially for words whosemeanings rely heavily on linguistic context.