I believe the OP has posted an ambiguous question,"The oldest drum set". Do you mean the oldest as it evolved in the 1890's w/ one man on a bass, snare, cymbal, & crude, improvised method of hitting the bass ? Or, do you mean the first official cataloged set, that probably came 20 years after the original invention ? Are you searching to give credit to a certain brand, or actually trying to date the first drum sets ? There are a number of makers in the 1890's that probably supplied the drums that double-drummers turned into sets.
The question is also ambiguous as to what is considered a set. Does it need toms & a floor tom, a hi-hat ? One post mentions the first set as 1942. This is 50 years later than my conception of the first set.