Droughts can cause significant damage to agriculture and water resources leading to severe economic losses. One of the most important aspects of drought management is to develop useful tools to forecast drought events, which could be helpful in mitigation strategies. The recent global trends in drought events reveal that climate change would be a dominant factor in influencing such events. The present study aims to understand this effect for the New South Wales (NSW) region of Australia, which has suffered from several droughts in recent decades. The understanding of the drought is usually carried out using a drought index, therefore the Standard Precipitation Evaporation Index (SPEI) was chosen as it uses both rainfall and temperature parameters in its calculation and has proven to better reflect drought. The drought index was calculated at various time scales (1, 3, 6, and 12 months) using a Climate Research Unit (CRU) dataset. The study focused on predicting the temporal aspect of the drought index using 13 different variables, of which eight were climatic drivers and sea surface temperature indices, and the remainder were various meteorological variables. The models used for forecasting were an artificial neural network (ANN) and support vector regression (SVR). The model was trained from 1901–2010 and tested for nine years (2011–2018), using three different performance metric scores (coefficient of determination (R2), root mean square error (RMSE), and mean absolute error (MAE). The results indicate that ANN was better than SVR in predicting temporal drought trends, with the highest R2 value of 0.86 for the former compared to 0.75 for the latter. The study also reveals that sea surface temperatures and the climatic index (Pacific Decadal Oscillation) do not have a significant effect on the temporal drought aspect. The present work can be considered as a first step, wherein we only study the temporal trends, towards the use of climatological variables and drought incidences for the NSW region.