Agreed; I fly the Saturday after Thanksgiving from BWI.
Check flights religiously as soon as they come out - try checking Tuesdays through Thursdays; that is when fares go down. They start heading up during the Friday through Monday time period. I think that is because people are normally home all together and can discuss their travel plans.
I finally booked my flight at 6:00 am on a Tuesday morning and it never got any lower than 89.00 that I booked. I was very pleased.
That being said, Thanksgiving is a bit different than Christmas week - it has gotta to be the busiest time all year for flying - because everyone takes off a lot of extra time. You have a few things working against you this year in particular. For instance, this year, we get the Friday before Christmas and New Year's as a govt. holiday. I will be off for ten days and only lose four days of vacation. Be mindful of that this year.
You are flying out on a Sunday, which is crazy busy, with people trying to get back to their jobs if they fly for business on Monday, if they only had Xmas holiday off.
The following Saturday will also be crazy busy, since a great deal of people who have taken off the entire week are going to come home a day early and have the extra day at home to get the kids back to school. I was told statistically on the Thanksgiving holiday weekend, about 2/3 of the people that stay at Disney leave that Saturday and the other 1/3 leave on a Sunday.
You most likely have picked the two worst days to fly in the entire year. It is all about supply and demand, the demand is going to be high and you are going to pay dearly for it.
You may want to try to head out the 27th and come back on a redeye on the following Monday, if you are looking for really deep discounts.