Green’s Dictionary of Slang

excellent, first-rate; smart, stylish.

1889		Gilbert Brigands in Standard 9 Nov. 3: We are dossy and neat From head to our feet [EDD].
1897		W.S. Maugham Liza of Lambeth (1966) 4: I say, ain’t she got up dossy?
1898		Harrington & LeBrunn [perf. Marie Lloyd] Everything in the Garden’s Lovely 🎵 We see a dossy youth go out in all his extra best / [...] / A pair of patents, pair of kids, and lovely flowered vest.
1905		Sporting Times 8 Apr. 1/5: A certain gentle and non-dossy librettist had his long grey mane clipped on Tuesday.
1981		P. White Flaws in the Glass 15: [T]hat bland, equable fellow with the blind blue eyes and dossy bow-tie.