We've stayed with discounts in March, so I'm not sure how much of a no-discount time it really is. We may have stayed under pins though, and what time in March can come into play.
You can stay absolutely anywhere on Disney property; until your little one turns 3, he doesn't count against the number of people in your room. Once he does turn 3, in addition to the resorts the pp mentioned, you can also stay at the Fort Wilderness Cabins.
You can book a room only reservation up to 499 days of your check-
out date. You will be charged a one night deposit equal to the highest rate in the current year. When the rate for your travel dates are released, your costs for the room will be adjusted, although your deposit amount will remain the same.
You can book a package as soon as the prices are release, traditionally in August of the previous year. So, 2012 rates should be released sometime August 2011. I'd book popular times of year, or hard to get rooms (some suites) as soon as you can to insure that you get the room you want.
You can always add a discount to any existing reservation, provided availability.
I agree with the poster who said do the math. "Free" dining is not free, because you do have to pay rack rate for the room AND tickets. There is usually, although not always, a discount code for room only reservations during the same time frame. Disney is also the most expensive place to purchase tickets from. Authorized discount ticket brokers (such as
Undercover Tourist--although there are many) are a better deal. On top of that, dining plans might not fit your dining style. Adding a dining plan, even when free, costs us more money than paying out of pocket.
Saving Money and Walt Disney World Dining Plans, gives you a good overview on how to run the numbers.