Milk is pretty easy. Mom brings that with her and has an almost endless supply.
You can coordinate with the Special Needs Department to have diapers, in the correct size, available for the child on an extended cruise.
Food wise: If it was like our kids and grandkids, once they started eating real food it was basically mushed up meats, vegetables and starches. My wife nor my daughter ever purchased "baby food." We have/had a great, battery operated, "musher" that makes great baby food. I think it now has been sold at a garage sale or buried in the baby stuff boxes in the basement. I loved playing with that thing.
I would think that the biggest problem is having to have a "kiddie corral"/playpen to keep the baby contained. The little guys disappear ever so easy.