Dear Mom of three:
I'm the family cruise editor here. We were just on HAL's Zuiderdam. I have a toddler and a nine year old. The toddler enjoyed the pool while my older daughter had fun in the youth program. We enjoyed the great service and good food too. However, as you know, HAL's youth program doesn't start until age five. Since you have a four year old, y ou might be better on the Paradise. That way, your pre-schooler can also participate in the youth program and you'll get some time just with your baby. Carnival has a very good youth program and the Paradise is a good choice for the families since other Carnival ships can get smoky at night.
You may want to read articles I've written that are posted on this section of the site on Camp Carnival and also Taking the Baby. The latter has lots of tips on things to consider before and during a cruise with an infant. I know, since my toddler went on three cruises already -- the first was last year when he was seven months old. You'll have to pack and bring a lot of stuff but it'll be worth it.
Make sure that you book a cabin with enough room for four beds plus a crib. We were recently in a cabin whereby you couldn't set up the crib if you pulled out the third bed. So my daughter ended up sleeping in bed with my husband and myself.
Let me know what you decide.
Smooth sailing,
Luisa Frey Gaynor