Adverse health events within families can harm children's development, including their early literacy. Using data from a longitudinal Wisconsin birth cohort, we estimated the spillover effect of younger siblings' gestational ages on older siblings' kindergarten-level literacy. We sampled 20,014 sibling pairs born during 2007-2010 who took Phonological Awareness Literacy Screening-Kindergarten tests during 2012-2016. Exposures were gestational age (completed weeks), preterm birth (gestational age <37 weeks), and very preterm birth (gestational age <32 weeks). We used gain-score regression -- a fixed effects strategy -- to estimate spillover effects. A one-week increase in younger siblings' gestational age improved the older siblings' test score by 0.011 SD (95% confidence interval: 0.001, 0.021 SD). The estimated spillover effect was larger among siblings whose mothers reported having a high school diploma/equivalent only (0.024 SD; 95% confidence interval: 0.004, 0.044 SD). The finding underscores the networked effects of one individual's early-life health shocks on their family members.