I've been on Carnival several times, a few before I had a child but recently with. It is not just for adults only at all. They have lots of kids programs and choices, in fact some of the best in my opinion. I took my 2 year old last year and she LOVED it!
If you want a more family feel don't cruise over spring break time. Other than that, I find Carnival to be fine for families. I have also sailed Princess,
Royal Caribbean, Costa, Cunard, etc. I can't say I have a favorite since it depends on where I want to go, how much I want to spend and what type of boat, etc.
I have a few more links to add that may help you figure things out. Depending on your child's age and your level of comfort there are many different cruise lines/styles.
http://www.cruisereviews.com/
reviews of cruises/lines
http://www.cruisemates.com/
Click under family crusing and the lady reviws the child friendly options in lots of detail.
http://www.portreviews.com/
This will help you review the ports you are considering.
http://www.cruisecompete.com/
This is the best deal in my opinion for booking on the web, but it's only really when you are ready to book. No real service, just best price. I like to play around with
http://www.vacationoutlet.com to find out boat info/prices when I am deciding.
If you haven't cruised before you may want to book with someone with a more personal touch and knowledge. Not sure who to recommend for that.
Jenn