1996 Toyota Tercel strange engine stalling problem

I bought this car recently and only discorvered the problem once I began driving it regularly. What happens is in the morning, and sometimes in the midday, my car will start okay but within a mile my car will stall when I come to a stop or slow. In detail, the car will drive fine until I come to a stop at a light or sign, the engine stalls and the battery light comes on. I can quickly turn the car back on, and after that I usually have no more problems for the whole drive. Somedays the car doesn't have this problem. The car drives great, but it does idle very very quietly. I'm thinking it's the IAC, but I can't be sure. Is this typically what a faulty IAC does?