My kids are 5 and 3. We sailed a few months back on Eurodam and the were preparing for a noro outbreak. The cruiselines handle this quite well. They stop all access to food service utensils/drinks etc. and have crew stationed at all these areas, including those dispensing hand sanitizer at the entrances.
I was soooooo worried that my kids would get something, but we were fine.
I will note that I am a fanatic with the hand sanitizer, and was santizing them constantly!.