Perhaps from daisy (the flower) or the name of Italian actress Eleonora Duse. The automobile manufacturer Duesenberg is often erroneously cited as the etymology of doozy; while seemingly sensical, the original usage of the latter predates the former by more than a decade. Doozy's origin is still unknown.
Audio (US) (file)
doozy (plural doozies)
- (US, informal) Something that is extraordinary: often troublesome, difficult or problematic, but sometimes extraordinary in a positive sense.
- Most of the test was easy, but the last question was a doozy.
- (slang, dated) Of high quality; remarkable; excellent. 
- 1903, Alfred Leon Kleberg, Slang Fables from Afar, page 83:
- As soon as the races were billed he began to evolve Schemes — one Doozy scheme followed the other...
- 2011, “Feeling Pinkie Keen”, in My Little Pony: Friendship is Magic:
- The hydra wasn't the doozy? How could it not be the doozy? What could be doozier than that?
- (slang, US, archaic) Sporty, ostentatious, flashy. 
- 1917, Elsie Warnock, “Terms of approbation and eulogy in American dialect speech”, in Dialect Notes, volume IV, page 21:
- Who was that doozy fellow I saw you with?
- 1920, Jane Barrett, “English review”, in High School Life, volume 21, page 531:
- Sweetie, do let me show you the dooziest little afternoon frock that Poiret designed for me in Paris.