We just (yesterday) got back from a cruise with our 3 yo and our 7 month old. We were on the Voyager of the Seas. There were quite a few babies on board and the entire staff doted on them. All the waiters stopped to play with the baby and hold him. We got so much attention with the baby with us. That being said, we always had the baby with us. The Voyager had a terrific program for our older son but notting for infants (not sure I could have left him anyway) so we did everything with baby in tow. As far as will your child be too young I'd say it depends on what you want to do. We did lots of hanging out at all the ports on beaches, taking our baby in the ocean for the first time etc. We didn't do any excursions, perfering to be able to move at our pace and be able to respond to our kids as needed, I'm sure there are a handful of outings you can go on though. We did feel like we were missing out on some of the stuff the ship/ports of call had to offer because of the baby but we figured that would be the case on any vacation with an infant. We enjoyed being at all these beautiful places with our sons and enjoyed the quiet pace their presense demanded (not that they were quite!) I'd say go for it!
Lisa