Population-scale single cell RNA-seq (scRNA-seq) datasets create unique opportunities for quantifying expression variation across individuals at the gene co-expression network level. Estimation of co-expression networks is well-established for bulk RNA-seq; however, single-cell measurements pose novel challenges due to technical limitations and noise levels of this technology. Gene-gene correlation estimates from scRNA-seq tend to be severely biased towards zero for genes with low and sparse expression. Here, we present Dozer to debias gene-gene correlation estimates from scRNA-seq datasets and accurately quantify network level variation across individuals. Dozer corrects correlation estimates in the general Poisson measurement model and provides a metric to quantify genes measured with high noise. Computational experiments establish that Dozer estimates are robust to mean expression levels of the genes and the sequencing depths of the datasets. Compared to alternatives, Dozer results in fewer false positive edges in the co-expression networks, yields more accurate estimates of network centrality measures and modules, and improves the faithfulness of networks estimated from separate batches of the datasets. We showcase unique analyses enabled by Dozer in two population-scale scRNA-seq applications. Co-expression network-based centrality analysis of multiple differentiating human induced pluripotent stem cell (iPSC) lines yields biologically coherent gene groups that are associated with iPSC differentiation efficiency. Application with population-scale scRNA-seq of oligodendrocytes from postmortem human tissues of Alzheimer disease and controls uniquely reveals co-expression modules of innate immune response with markedly different co-expression levels between the diagnoses. Dozer represents an important advance in estimating personalized co-expression networks from scRNA-seq data.