Long-range forecasting of intermittent streamflow in semi-arid Australia poses a number of major challenges. One of the challenges relates to modelling zero, skewed, non-stationary, and non-linear data. To address this, a statistical model to forecast streamflow up to 12 months ahead is applied to five semi-arid catchments in South Western Queensland. The model uses logistic regression through Generalised Additive Models for Location, Scale and Shape (GAMLSS) to determine the probability of flow occurring in any of the systems. We then use the same regression framework in combination with a right-skewed distribution, the Box-Cox t distribution, to model the intensity (depth) of the non-zero streamflows. Time, seasonality and climate indices, describing the Pacific and Indian Ocean sea surface temperatures, are tested as covariates in the GAMLSS model to make probabilistic 6 and 12-month forecasts of the occurrence and intensity of streamflow. The output reveals that in the study region the occurrence and variability of flow is driven by sea surface temperatures and therefore forecasts can be made with some skill.