According to the Oxford dictionary, the origin of higgledy-piggledy dates from the late 16th century and is a rhyming jingle, probably with reference to the difficulties of herding pigs.
The definition in the Oxford Dictionary says that the word describes something ‘in confusion or disorder’, which means I have always been wrong in what I thought it meant. For me, it just meant jumbled up – not confused – just not in order. There may be no difference, but confusion seems to indicate that the desire was for order but it was not fulfilled. Whereas for me, higgledy-piggledy just means out of order – with no burning desire for order that has been thwarted or unfulfilled.
The Etymology site at Etymonline mentions other similar double words. I never thought about it but I know all these and I guess you do too: hanky-panky, hocus-pocus, hurly-burly, hodge-podge, harum-scarum, helter-skelter, flim-flam, fiddle-faddle, hotch-potch, hum-drum, tittle-tattle, shilly-shally, topsy-turvy.