Mark,
I haven't shipped a camper but last winter did ship a conversion van from Michigan to Florida (when gas prices were less) and the cheapest carrier I was able to find charged $3800 - 1 way.
They picked it up at my sister's house 1 hour north of Detroit, and dropped it at Fort Myers airport.
Weight would be less, but it would take up the same amount of space I imagine.
Just fyi..