I wouldn't take a child that age backpacking round India but really can't see the problem with Goa and Mumbai!
My Dd went to Malaysia at 18 months, Sri Lanka at 2 1/2, then Goa at 3, and 4, and 5! I don't think she even got a stomach upset. I agree you do need to be sensible.
Agree bottled water. I never sterilised bottles in Malaysia at 18 months, and just bought cartons of milk. You can buy them easily in Goa too. Depends how fussy your child is I guess. My DD wasn't bothered if it was UHT or not cow's milk (never quite sure what sort of milk it is in India!). On the other hand, we have just been away with 5 month old DS and it was no trouble to take Milton tablets, buy a cheap washing up bowl and sterilise the bottles.
I would take some baby food for travelling but presumably DC can eat rice, veg, naan bread, cheese sandwiches, even if they don't like curries?
My blond haired blue eyed DD gets so much attention in Goa, with people wanting photos with her and talk to her or touch her. It can get a bit wearing and I didn't mind if a family wanted a photo of her with their children but sometimes men would try to take photos of her or want a photo of her with them. This just seemed, at best, a bit weird so we did keep an eye out for people trying to sneak photos and stood in their way.
Make sure you have any jabs your child needs and get advice on malaria tablets. If recommended you will have great fun trying to get a 15 month old to take them! We crushed them up in honey when DD was younger.
Take loads of factor 50 sunblock - what I have seen for sale in Goa is often lower factor and can look as thought it has been hanging around for a while.
The sea in Goa can be very rough with really strong currents. You may just be paddling but if you do go in deeper holding your DC make sure they have armbands and you hold on very tightly.
Most places to eat won't have highchairs. We bought an inflatable booster seat from Argos that was very useful.
A folded up MacLaren pushchair fits perfectly on the shelf above the seat at the back of a Tuk Tuk!