I've travelled to the Caymans a couple of times with young kids, and never had a problem bringing in food--even lunchables in our carry-ons. I honestly don't think anyone checked anything when we arrived. Like other posters said, coming back into the states is another story. But I also agree that grocery stores there have just about everything you're used to here--we got the same brands of all the same things the kids liked (cereal, mac n cheese and stuff--they were too old for babyfood). Depending upon how long you'll be there for, you may not want to carry enough with you for your whole trip. When travelling with kids, I'm a big one for packing as light as possible--I only bring enough diapers, food, etc, to get through the day we travel, then plan on stopping by the store within 24 hours of arrival. The less you have to carry, the better.
Anything in glass jars will have to be checked, since they won't allow it on the planes these days. Glass also gets heavy quickly, and can break, so watch how you pack if you do decide to bring food with. Also remember that checked luggage does sometimes get delayed--on one trip to the caymans, my bag arrived 2 days after me. It wasn't tragic--I bought a suit, shorts, and t-shirt at the hotel gift shop, and was fine--but you wouldn't want to be counting on feeding your kid out of luggage that has been lost.
Have fun on your trip--the Caymans are a very kid-friendly place to travel. I'm sure you'll have a great time!