Hi, my sister, hubby, and her 2 kids (19 mo and 3 mo) just went with us on Celebrity Galaxy. I think things worked out fine for them, though infants need to be 6 months to have a babysitter, so the baby was with them the whole time. We had late seating (8:30) and they booked a sitter on the first night for the whole from 9 to midnight (9 pm was the earliest that they would let them get a sitter). One of the adults would stay in the room till the sitter came and the other would order for both of them. By 9 pm, we were just about through with our appetizer, but the waiter always delivered a hot appetizer to my sister or husband. It cost $8 per hour, and they had the same babysitter the whole week, who was very caring and really loved kids. Apparantly, it's women who work in the "Pantry" who babysit, and they get off work at 9. The first couple of nights, my sister would stop in to see what they were up to and always was pleased. Also, little ones can play in the kids' club with their parents, but no diapers in the ball pits.
We have a 4 and 7 year old and things are definitely easier once they can use the kid's club, though our kid's primarily used it in the evening (7:30 to 10), and on this cruise with the late seating, they would join us for dessert at 10 (one of us would go get them). On a cruise we took earlier this year, we had early seating at 6 pm, so they would eat and then we'd take them to the kids club right when it opened at 7 (on Royal Caribbean) and when we got back to the table, our entree would there. It worked out great.
There's plenty of other dining options for the kids too. You can order room service, get pizza, eat at the afternoon tea (sandwiches and desserts), so you don't have to take them to the dining room. Every breakfast and lunch we ate in the buffet restaurant, so there was no waiting.
I wouldn't rule out a cruise with a little one. Your whole lifestyle has adjusted to having a little one. It's no different on a cruise. It's still a wonderful vacation, with great beaches and water (you should have seen my 19 mo old niece in the water!). You just need to find what works for you on the ship, just like at home! I know my sister and are already planning a cruise in 3 years when her 3 month old turns 3!