The gini of Indonesia, at ~37, isn't low, but it isn't particularly high either. Below Malaysia, China, and the Philippines, but above Thailand. Mobility is hard to track at Indonesia's level of development. All I could find was this study, which suggests relatively high educational mobility in the Jakarta "slums" [1] and this study that suggests that Indonesia is an outlier in terms of having high mobility relative to its level of inequality [2].
[1] https://www.adb.org/sites/default/files/publication/488961/a... [2] https://www.wider.unu.edu/sites/default/files/Publications/W...