We spent 4 months in India when our oldest was 18 months. Remember to check vaccines early, the BCG needs to be given 6 months in advance if I remember correctly, and they need two dozes. Be careful to find out if you need any malaria prophylactics. They ruined my sons appetite totally, so it was a bit of a struggle over meal times.
We stayed in Bangalore, then went to Trivandrum and headed south along the coast in Kerala. We hired a car and drove to Cochin, then did a back water cruise, drove to Munnar to look at the teaplantations and explore the "highlands" and spice plantations, before heading back to Bangalore, then Sri Lanka for a small holiday on the way back.
My best advice to you is to pack torch light and batteries, bring some moscito repellent but stock up locally and use the electric moscito repellents in the room and follow the instructions carefully. Bring long thin trousers and long sleeved shirts for evening, you dont want bugs crawling in/moscitos biting. Bring high factor sunlotion with you.
Bring any nappies you plan to use, we could not find nappies locally, children either went without (yes, accidents happened both kinds, even on restaurant floors) or wore cloth nappies. It is hot and humid, so I suggest long t shirt and no nappies for day wear, or just put shorts on when going to town. Take good quality nappy rash cream, like Methanium and Bepanthen. Bring wet wipes, antibac wipes, etc.
Having said this, Goa is touristy, so you may be able to find all this locally.