There is tremendous interest in estimating county-level disease prevalence. This is often done via model-based small-area estimation using survey data. However, for conditions with low prevalence (i.e., rare disease), counties with high fraction of zero counts in surveys are common. To account for counties with excess zero counts, we proposed a Bayesian hierarchical regression, modeling prevalence as a mixture of a beta binomial and a zero point mass. We denoted this Bayesian model with zero-inflated beta distribution as BZBB. Accounting for the sampling design through sampling weights and using historical data to derive our prior, we estimated county-level prevalence of vision impairment using Behavioral Risk Factor Surveillance System data. We evaluated our estimates with American Community Survey results and simulation data. We showed that BZBB yielded less bias and smaller variance than estimates based on a binomial distribution, a common approach to this problem.