You can't. Amtrak's auto train service only runs from Lorton VA (outside of DC) to Florida. You could drive down to DC and board the train, though. Beats driving the whole way!
There are companies that will transport your car on a car carrier like when they deliver new cars to a dealer. Check your local Yellow Pages.
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Other people asked questions on various topics, and are still waiting for answer. Would be great if you can take a sec and answer them