Nothing for a 1 year old to do in Disney?She will be in 1 year old heaven. The characters im sure she will love. There are plenty of gentle rides for the whole family (eg its a small small world). Also you have some great pools in all the resorts. She would also love Blizzard Beach, they have a kids area which i am sure will keep her entertained. The CMs love liitle kids, she will get plenty of attention. You also will get a huge kick out of watching her reactions to it all.
As far as airlines go, we always travel Virgin and have been very satisfied. IMHO any airline flying to Florida is going to be kid/baby friendly.