Droughts can cause significant damage to agriculture and water resources, leading to severe economic losses and loss of life. One of the most important aspect is to develop effective tools to forecast drought events that could be helpful in mitigation strategies. The understanding of droughts has become more challenging because of the effect of climate change, urbanization and water management; therefore, the present study aims to forecast droughts by determining an appropriate index and analyzing its changes, using climate variables. The work was conducted in three different phases, first being the determination of Standard Precipitation Evaporation Index (SPEI), using global climatic dataset of Climate Research Unit (CRU) from 1901–2018. The indices are calculated at different monthly intervals which could depict short-term or long-term changes, and the index value represents different drought classes, ranging from extremely dry to extremely wet. However, the present study was focused only on forecasting at short-term scales for New South Wales (NSW) region of Australia and was conducted at two different time scales, one month and three months. The second phase involved dividing the data into three sample sizes, training (1901–2010), testing (2011–2015) and validation (2016–2018). Finally, a machine learning approach, Random Forest (RF), was used to train and test the data, using various climatic variables, e.g., rainfall, potential evapotranspiration, cloud cover, vapor pressure and temperature (maximum, minimum and mean). The final phase was to analyze the performance of the model based on statistical metrics and drought classes. Regarding this, the performance of the testing period was conducted by using statistical metrics, Coefficient of Determination (R2) and Root-Mean-Square-Error (RMSE) method. The performance of the model showed a considerably higher value of R2 for both the time scales. However, statistical metrics analyzes the variation between the predicted and observed index values, and it does not consider the drought classes. Therefore, the variation in predicted and observed SPEI values were analyzed based on different drought classes, which were validated by using the Receiver Operating Characteristic (ROC)-based Area under the Curve (AUC) approach. The results reveal that the classification of drought classes during the validation period had an AUC of 0.82 for SPEI 1 case and 0.84 for SPEI 3 case. The study depicts that the Random Forest model can perform both regression and classification analysis for drought studies in NSW. The work also suggests that the performance of any model for drought forecasting should not be limited only through statistical metrics, but also by examining the variation in terms of drought characteristics.