Air Carrier Captain reported initiating own go around at 100 feet as proceeding departure was still on the runway. ATC provided vectors and the aircraft landed safely.

Narrative

Missed approach due to traffic on runway taking off with insufficient interval. Flying visual approach to IND; when checking in with IND Tower and told to continue approach". Then Aircraft Y cleared onto runway for takeoff did not start takeoff roll until our aircraft was inside 300 ft. We were at approximately 100 ft. with Aircraft Y still on the runway and initiated our own missed approach. Tower directed that we take a left turn 30 degrees. Had we not conducted the missed app it appeared that both aircraft would have been on the runway at the same time. While being vectored for subsequent approach I asked for and was given the phone number for the IND Tower Supervisor. Once on the ground; I contacted the Tower supervisor and suggested that they pull the tapes and conduct and evaluation and training with respect to these events; as it was; in my opinion; grossly unsafe to allow the approach to continue; and that the missed approach should have been called for well before we initiated our own missed approach."