score:10
I searched for infant in the Carnival FAQs and found the following (in order of relevance to you)
So it seems your answer on Carnival is NO. They're not equipped and you're not allowed. I didn't search other cruise lines, but since the rationale for not allowing them is worry that such a small baby could get sick very quickly, I suspect you'll find the same elsewhere.
Upvote:1
Disney Cruise Line also disallows children under 6 months (or 12 months for certain longer itineraries) beginning last year.
http://disneycruiselineblog.com/2014/07/disney-cruise-lines-infant-policy-changes-effective-7182014/