Understanding potential changes in future rainfall and their local impacts on Australian communities can inform adaptation decisions worth billions of dollars in insurance, agriculture, and other sectors. This understanding relies on downscaling a large ensemble of coarse Global Climate Models (GCMs), our primary tool for simulating future climate. However, the prohibitively high computational cost of downscaling has been a significant barrier. In response, this study develops a cost-efficient downscaling framework for daily precipitation using Long Short-Term Memory (LSTM) models. The models are trained with ERA5 reanalysis data and a customized quantile loss function to better capture precipitation extremes. The framework is employed to downscale precipitation from a GCM member of the CMIP6 ensemble. We demonstrate the skills of the downscaling models to capture spatial and temporal characteristics of precipitation. We also explore regional future changes in precipitation extremes projected by the downscaled GCM. In general, this framework will enable the generation of a large ensemble of regional future projections for Australian rainfall. This will further enhance the assessment of likely climate risks and the quantification of their uncertainties.