Green’s Dictionary of Slang

a muddle, a surprising occurance.

1810		C. Dibdin Yngr Spectre Knight 12: Here’s a rumfoozle for you – to come all the way from Ireland to serve a Scotch Master who was kilt by a French Foreigner; and then to have my sweetheart stole away by an English Rival.
1896		Leeds Times 16 May 8/5: the get-up of the gentleman in ‘Rumfoozle Rumtitay’ is a trifle overdone for good taste.