I'll third the recommendation to check out
http://www.cruisecritic.com for information... it's to cruising what the DISBoards are to WDW.
I see you're in Virginia. There are many cruiselines doing cruises from other departure ports other than Miami on the East Coast. We live in CT and have found it to be much easier and more cost effective to cruise out of NY/NJ (to the Caribbean) than to fly to Miami. I know there are cruises out of Baltimore and I think there are some out of NC/SC, as well. Consider driving to one of the closest departure ports.
With a family that large, your most cost effective choice would be two side-by-side cabins. Choose interior cabins lower in the ship to save a bundle... you'll get the same service and amenities as folks who spend a lot more.
The least expensive time of year to go is the fall because it's Hurricane Season. If you choose to go then, get
trip insurance (
http://www.insuremytrip.com). In fact, it's always a good idea to get trip insurance when you go on a cruise.
At one time, Norwegian Cruise Line was not charging any fare (just taxes) for a child under the age of 2... I don't know if that is still their policy. Other cruise lines will charge you the full fare for your baby. Also, be warned, there are no cruiselines that I know of that will take the baby in the children's programs or will babysit a child of that age in your cabin.
Good Luck with your planning!