Have you booked anything?
A few suggestions:
Have you considered flying to Florida? Some of the low fare airlines like Southwest, can get you to Florida for cheaper (or close to the cost of driving). You will have waaaaay more options out of Florida.
Have you considered HAL? We recently sailed HAL Eurodam and had a pretty good time! You can read my review on this site - go to Cruise Reviews and Member Reviews. One of the reasons I recommend HAL for you, is that I recall them having vegertarian particularly Indian vegetarian options at every MDR meal.
Most ships have Indian chefs. If you ask the Maitre D, they can arrange to have special Indian meals cooked for you. While I have never done this, we have friends who request Goan food on every sailing they take. And the Chefs spoil them! i think for some of them it is a priveledge to cook their native food for you.
If you're considering a Carnival sailing, I'd stick with one of the newer ships like Magic or Dream .... but you'll have to sail out of Florida for those.
We're a young family with two young kids (5 and 4). With our kids, we've sailed HAL and Carnival, and we're soon taking them on a Royal Cruise. If you have any questions .... ask away!