Hi Sara!
Disney's Art of Animation Resort is so well themed, and appeals to kids of all ages. It is also a Value Resort, which means a stay at
Disney's Boardwalk Inn or
Disney's Animal Kingdom Lodge will be more expensive. For your 3 year old, I would highly recommend Animal Kingdom Lodge. The animals will be captivating, and the resort is just amazing. Of course, you can't go wrong with any Walt Disney World Resort hotel. They are all themed wonderfully, and each holds its own appeal.
Of the 3 months you mentioned, mid-January will most likely have the lowest crowd levels. It is also much cooler then, so keep that in mind. Crowds will pick up around the Friday before Martin Luther King Jr. Day, so avoid that since crowds are a concern for you. Early November and early December are also good times so you really can't go wrong. Whatever you decide, go with a plan so you can make the best use of your time.
I wish you a MAGICAL vacation!
-Jacqui