There aren't any nonstops from JFK to CAE.

My suggestion is to get a taxi or the airport bus to LGA airport. The ride should not be more than 30 minutes and will cost $13 by bus. I have not used a taxi before so I don't know that cost.

At 17:35, there is a nonstop Delta Connection flight from LGA to CAE and it looks open right now for both the first and second of December.