In this paper, we consider an extension of the classical discrete-time dual risk model, in which the first-order integer-valued autoregressive (INAR(1)) process with Poisson distributed innovations is utilized to fit the temporal dependence between the number of gains for each period. We derive the explicit expression for a function that allows us to find the Lundberg adjustment coefficient and obtain the Lundberg approximation formula for ruin probability. Some numerical examples are provided to illustrate our main results.