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A rainfall-streamflow model is proposed, in which a downscaled rainfall series and its wavelet-based decomposed sub-series at optimum lags were used as covariates in GAMLSS (Generalized Additive Model in Location, Scale and Shape). GAMLSS is applied in climate change impact assessment using CMIP5 general climate model to simulate daily streamflow in three sub-catchments of the Onkaparinga catchment, South Australia. The Spearman correlation and Nash-Sutcliffe efficiency between the observed and median simulated streamflow values were high and comparable for both the calibration and validation periods for each sub-catchment. We show that the GAMLSS has the capability to capture non-stationarity in the rainfall-streamflow process. It was also observed that the use of wavelet-based decomposed rainfall sub-series with optimum lags as covariates in the GAMLSS model captures the underlying physics of the rainfall-streamflow process. The development and application of an empirical rainfall-streamflow model that can be used to assess the impact of catchment-scale climate change on streamflow is demonstrated.