This study examined whether the behaviour of Internet search users obtained from Google Trends contributes to the forecasting of two Australian macroeconomic indicators: monthly unemployment rate and monthly number of short-term visitors. We assessed the performance of traditional time series linear regression (SARIMA) against a widely used machine learning technique (support vector regression) and a deep learning technique (convolutional neural network) in forecasting both indicators across different data settings. Our study focused on the out-of-sample forecasting performance of the SARIMA, SVR, and CNN models and forecasting the two Australian indicators. We adopted a multi-step approach to compare the performance of the models built over different forecasting horizons and assessed the impact of incorporating Google Trends data in the modelling process. Our approach supports a data-driven framework, which reduces the number of features prior to selecting the best-performing model. The experiments showed that incorporating Internet search data in the forecasting models improved the forecasting accuracy and that the results were dependent on the forecasting horizon, as well as the technique. To the best of our knowledge, this study is the first to assess the usefulness of Google search data in the context of these two economic variables. An extensive comparison of the performance of traditional and machine learning techniques on different data settings was conducted to enable the selection of an efficient model, including the forecasting technique, horizon, and modelling features.