I will be there in 4 weeks with DSister and DBIL (in a 2 bedroom villa) I will be brining DS (age 13 1/2 months) and DSister will be brining her daugher (age 23 1/2 months). So, in about 5 weeks I can probably answer your questions well about a 2 yr old.
My DS has already been twice - first at 6 months, second at 8 months. We were there Oct and Dec, so it was a bit cooler (mid 80's, low humidity in Dec). DS did great. He loved MK. He loved all the rides we took him on - IASW, Pooh, Peter Pan, Buzz, etc (pretty much everything in Fantasyland and then some). He slepted through Pirates. He nursed through Haunted Mansion and Mickey's Philharmagic - the theme was that on the darker rides, he either nursed or napped.
He loved the Spectromagic parade, he loved watching other kids, balloons, etc. Overall, he was very happy, and it was a really easy age. He had no fear of the characters - he loved the fuzzy ones and was laughing as they visited with him.
We had a stroller - I would recommend a very good sun shade for your stroller, plus a stroller fan. Also, you have to park the stroller a lot for the lines, so I had a hip carrier just to make it a bit easier, and keep my hands free when needed.
Otherwise, the Baby Care centers were great when we needed a break, needed to feed him, or change a diaper. There is one in each park. MK was great, Epcot was nice, DS was OK. I have not yet been to AK with him, so can't comment on the Baby Care there, but others have said its nice.
At 8 months, DS was happy enough sleeping in the stroller, and seemed to "cat nap" on dark rides, walking around, etc. Food wasn't an issue for him - I just brought some basics with me, plus I was still nursing. Overall, it was a very easy age to take a baby. I expect that this upcoming trip will be a bit more challenging, but still fun.