We always learned that doozy came from Duesenberg, which was an especially impressive car. Halfway recalled reading a debunk of the origin.
The Duesenberg brothers started out as engineers at Maytag, which made gas-powered washers before it switched to electric. They departed and created their own car in 1920. It would have taken a few years for the car to establish its own slang.
Google’s Ngram thingie does an instant debunk. Here’s doozy from the start of Ngram to 1920. The word was starting to gain popularity before the car reached the market, so it was available to describe the car.
The peak in 1820 seems to come from one peculiar made-up instance, which was quoted in various literary reviews.
Polistra's Mill 