Hi Amy,
I will be there as well running the half. Ironically I will be staying at Animal Kingdom with my 3 year old, but I would highly recommend the Polynesian. I am only staying at Animal Kingdom because I own a Disney Vacation Club share at that resort.
For you, the Polynesian will offer very fast and convenient access to the Magic Kingdom, which will most likely become your daughter's favorite park. If you travel with a stroller, the monorail will be much easy to use than a bus. At the Polynesian, you have the option of having a character breakfast or easily traveling to one of the other monorail resorts for one of their character dining experiences. I would recommend
Chef Mickey's at the Contemporary. Animal Kingdom has no character dining and traveling from there to another resort can be slightly difficult.
If someone in your family is running the marathon they will be very happy staying at a monorail resort. The buses can become a bit crowded at 4:00 in the morning. It is very easy to walk out of the Polynesian, hop on the monorail and head over to the starting line in Epcot. I stayed at a monorail resort for the 07 marathon and I had a much better experience then a friend who traveled to the starting line via a bus from the All Star.
I would recommend saving Animal Kingdom for your next trip to WDW. I'm sure you'll have so much fun in January that you'll be back again soon.
Have a great vacation,
Michelle