What's the very first sorted column in the design?
GetAllDocumentsByKey() can filter out the calendar entries for a specific date.
Once you're there, the count of documents is pretty small, and you can look at the AppointmentType to find All-Day events.
You can also GetDocumentByKey() 'til you find the first document on/after 1/1/2014, and then continue forward from that document 'til you reach the end of the calendar. Keep in mind you can get a lot of future documents on a calendar, when it has repeating documents.