Hi Linda,
Thank you so much for visiting the Disney Parks Moms Panel with your question. My family and I spent New Year's Eve at Walt Disney World last year, and we had a great time! Although special events for New Year's Eve 2014 have not yet been released, we can look to past years to see what might be offered. Please do know that these might change for 2014.
To my knowledge, there have not been fireworks shows at Downtown Disney on New Year's Eve. Last year, fireworks rung in the New Year at Disney's Hollywood Studios, Magic Kingdom Park, and Epcot. There was a special party at DisneyQuest at Downtown Disney on New Year's Eve last year which included refreshments, characters, and a New Year's Eve countdown. I suggest keeping an eye on the
Disney Parks Blog for announcements about New Year's Eve events for this year.
As to hours of operation for the boats between Downtown Disney and Disney's Saratoga Springs Resort & Spa, I spoke with a cast member who told me that the boats typically run about one hour after closing time at Downtown Disney. I suggest that you check with a cast member at the front desk or on the boat when you arrive to see if this would change for New Year's Eve.
I hope that these thoughts are helpful for you, Linda. Have a great time planning your magical vacation, and please do not hesitate to ask if you have any further questions.