I brought pre made, pureed baby food when my son was that age just in case. At least these days there is plenty of it in plastic for easier traveling than glass. I use only bottled water (can buy big bottles from the bar aboard ship) for my kids when aboard ship.
Most mini frigs are cooling boxes so they're great for keeping water cold but I wouldn't want to keep formula or dairy in them overnight. I always brought powdered formula when cruising and just mixed it with bottled water as needed.
I've written an article, "Bringing the Baby" which would be helpful for you to read. It's on the main family cruise page of this site.
Luisa Frey Gaynor