The Carnival website should give you square footage. Their cabins are somewhat larger than most cruise lines.
I would suggest letting the 7 year old try out Camp Carnival. Kids seem to be well supervised and have a ball at the same time. I'm not sure if they still offer it, but since the baby is too young for the organized stuff, you used to be able to hire a staff member as a baby sitter. Maybe have a romantic night out. Nicer in some ways than back home, since they can always get in touch with you on the ship if they need to, so you can truly relax a bit.