This will be our third year going down for my older son's birthday (turning 4). His birthday is on the 4th. We're headed down on the 30th this year. The crowds have always been less crazy for this time of the year with one exception--when they're taping the Christmas Parade at MK. They do it on that Saturday and MK is a MADHOUSE. I'd say stay away from MK that day. Other than that, you should be alright.
The hotels are usually sold out for two reasons:
1. It's the cheapest time of the year for us DVCers to come down (points-wise).
2. This is the time Disney does a lot of refurbishing for attractions AND the hotels. So there aren't as many rooms available anyway.
The weather is always better than the summer and crowds are lower (compared to busier times). There are always crowds at DW.
Enjoy your trip!