To the last poster, there will probably be a high chair the first night, but you could let the wait staff know that you are not using the high chair and they will not bring it subsequent nights.
To the original poster, I wondered the same thing when I cruised with my 8 month old. Until I was on the cruise, they had to work double for my infant (crackers, mac and cheese) plus he left a huge mess. I felt badly about the mess, but if he didn't have crackers and food to try to eat, then dh and I could not eat. We ended up tipping extra. Depending on the babies age, they might not be eating many solids (if any), so there might not be any need to tip very much. I'd wait to decide how much to tip until you get to your cruise. It will be obvious if you get waitstaff that goes beyond the call of duty. We had a terrific waitstaff. They were so happy to play with the baby and keep him satisfied it made our experience that much better. There was no doubt that they deserved their tip. In my opinion, a good waiter will make it obvious if they deserve the tip.
Have fun -- I love cruising with babies!!!