My child has food allergies (egg, dairy and seafood). We went on a cruise with Royal Carribean in Jan when she was 2 yo. I called up RC in advance to request for special meals for her, which they did accommodated really well. The chef met us when we first visited the dining room to find out what are her fav food and preferences. The only issue is such made to order meals are only served in the dining hall, so you can't have them in the buffet restaurant. Do note that RC specifically mentioned that they would not be able to provide baby food (purée). So you may want to tell them that your child can take normal adult food like porridge without the allergens.
You can't bring rice cooker onboard a cruise, it will be confiscated and returned when you disembarked. This is to prevent short circuits and fires on the ship.