The Gaia DR3 has provided a large sample of more than 6.6 million quasar candidates with high completeness but low purity. Previous work on the CatNorth quasar candidate catalog has shown that including external multiband data and applying machine learning methods can efficiently purify the original Gaia DR3 quasar candidate catalog and improve the redshift estimates. In this paper, we extend the Gaia DR3 quasar candidate selection to the Southern Hemisphere using data from SkyMapper, CatWISE, and Visible and Infrared Survey Telescope for Astronomy surveys. We train an XGBoost classifier on a unified set of high-confidence stars and spectroscopically confirmed quasars and galaxies. For sources with available Gaia BP/RP spectra, spectroscopic redshifts are derived using a pretrained convolutional neural network (RegNet). We also train an ensemble photometric redshift estimation model based on XGBoost, TabNet, and FT-Transformer, achieving a root mean square error of 0.2256 and a normalized median absolute deviation of 0.0187 on the validation set. By merging CatSouth with the previously published CatNorth catalog, we construct the unified all-sky CatGlobe catalog with nearly 1.9 million sources at G<21, providing a comprehensive and high-purity quasar candidate sample for future spectroscopic and cosmological investigations.