The Jupiter and Lake Worth Railroad was a 7.5 mile narrow gauge (3') connection between the south end of the Indian River at Jupiter Inlet and Lake Worth. It carried passangers form the steamboats traveling south from Melbourne and Titusville to connect with boats on Lake Worth. It was completed in 1889 and the end came in 1895 when it was bypassed by Henry Flagler's Florida East Coast Railroad.
More information and photos at: http://www.taplines.net/jalw/jalwry.htm
A very long, scholarly report "Retracing the Celestial Railroad" by Geoffrey Lynfield is found here:
Jupiter is about 30 miles south.
Here is a photo of The St. Lucie steamboat on the Indian River at Eden, just east of my location.
From the Library of Congress