Green’s Dictionary of Slang

a soft felt hat with a wide brim.

1896		Inquirer & Commercial News (Perth) 19 June 5/9: The defendant carried a ‘Dr Jim’ white hat.
1896		Dundee Courier 3 Aug. 4/6: A flash young gentleman, rigged out with a ‘Dr Jim hat’.
1897		Amer. Hatter 27 39: Blaylock & Blynn have issued the new soft hat of the season, ‘The Cairo,’ which is even more of a success than the ‘Dr. Jim’ hat that they introduced last season.
1899		S. Aus. Register (Adelaide) 25 Feb. 10/6: The Dr Jim hat [...] was donned by many an admirer of Dr Jameson.
1904		Eve. Post (Dundee) 6 Sept. 2/3: One of the Reillys tried on a ‘Dr Jim hat’ [...] to see how it would suit him.
1905		Sydney Morn. Herald 28 Feb. 8/3: She saw a lot of trouble for him in connection with the girl and a man in a ‘Dr Jim’ hat.
1909		J. Ware Passing Eng. of the Victorian Era 112/2: Dr Jim (Peoples’, 1896). A soft felt hat, with wide brim. [...] Upon the arrival, late in 1896, of Dr Jameson from the Transvaal, the wide rim of his soft Africander felt was at once accepted. For some weeks these models were called Jemmysons, but the hero in question becoming more popular as Dr Jim, the wide soft felter became a Dr Jim – very soon reduced to Jimmunt, sometimes a Jimkwim – the outcome of a coalescing between the earlier and later titles.
1911		Barrier Miner (Broken Hill, NSW) 8 Aug. 4/7: He removed his hardhitter from the sleeper’s head, upon which he placed his Dr Jim.
1914		Western Times 2 Mar. 4/6: The man wore a Dr Jim hat.