A well known wooden toy from the past, transferred to 3D printing.

http://www.instructables.com/id/Wooden-Toy-Snake/
Print the body 45 degrees rotated around the z-axis, to fit on the bed. If necessary, scale it down. The end disks of the body have half the thickness of the other disks, so more body elements can be glued together. Prints well in PLA without support. The body has zero infill but be prepared for a long print session. Tail and head are printed with the flat side down. For these two parts a low infill (10-20%) is O.K.
In case you want to play around with it, the OpenSCAD files are included. If you can design a more realistic head, please upload it. I am a simple engineer, not an artist.
If two disks break apart, sand the surfaces and bond them together. There will still be a lot of flexibility left.