This paper analyzes the block error rate (BLER) of hybrid automatic repeat request with incremental redundancy (HARQ-IR) assisted short packet communications. The small packet size leads to the occurrence of the time correlation among HARQ rounds. To accurately capture the effect of time correlation, a general correlated Nakagami-m fading channel model is first developed. However, the channel correlation, multiple transmissions, and finite blocklength information theory extremely challenge the analysis of BLER. To confront this, the average BLER is derived in a compact form by capitalizing on linearization approximation and conditional Laplace transform. To reveal more insights, the asymptotic BLER in high signal-to-noise ratio is obtained in a simple form. It is disclosed that full time diversity can be achieved by the proposed HARQ-IR-aided scheme. This justifies the feasibility of using retransmissions to offer reliable short packet communications. The numerical results finally corroborate the validity of our analysis.