I think the complexity is pretty much what you wish it to be. I've seen
limberjacks that range from 10" to 18" in height, with and without
fancy joints, but all of them have jointed knees, hips and shoulders
(easily done with axle dowels with a cap style end). Stick a dowel
about 2/3 of the way up the back and make a board large enough to be
sat upon and bounced by hand while the kid holds the jack's stick.
Great combination toy and rhythm instrument.
Paint or don't paint, finish or don't finish. I'd use something like
soft maple or poplar for the jack (traditionally, in Appalachia, it is
done in cherry or walnut and left unfinished), and maybe poplar or pine
for the percussion board.
Sounds like time for someone to do an article on the subject, fer
pete's sake. I found a sufficiency of photos, but no plans other than
what you found.
By the way, the limberjack is not always classed as a toy. A bit west
of here, it's a musical instrument usually played by adults.