It depends on when you are traveling. Amtrak fares are, naturally, highest in summer and around holidays, so try to avoid these periods. However, in celebration of Amtrak's 30th birthday (May 1, 2001) they have a 30% off sale which was just extended through August. This discount is applicable to the trip you want. Also, if you wanted to drive to Lorton, VA. and take the train from there (Auto-Train), kids get 75% off in the same promotion. Finally, regularly check Railsale on Amtrak's website (updated every Monday I think) for some BIG savings (try Philadelphia to Chicago for $32). There's nothing there right now along your route, but it does pay to keep checking.
You have a choice of two direct trains from New York to Orlando, the Silver Star and Silver Meteor. Both have full dining cars, and sleeping cars if you want to go first class. The Silver Palm does not serve the Disney area (a connecting bus is required). Note that if you are taking a taxi from the train station to WDW, the station in Kissimmee is closer.
I hope this helps. Have a great trip.