From Sanskrit द्राविड (drāviḍa) + -ian. *tamiḻ > *damiḷ > damiḷa- / damila- and further, with the intrusive, 'hypercorrect' (or perhaps analogical) -r-, into dr(a/ā)viḍa.
Practice speaking and memorizing "Dravidian" and many other words and sentences in English.