This curious reduplicated noun turns up from time to time, almost always in British sources. Its meaning may be deduced from a couple of examples:
He said he’d think nothing of quaffing ale all night and coming home at 5 a.m., smashing windows. He said he was a bit of a roister-doister, not like these white-livered people today who can’t hold their drink.
Wyrd Sisters, by Terry Pratchett, 1988.
I am due to talk to the veteran Hollywood roister-doister — a serially married, reformed and relapsed alcoholic, who was famously arrested, wild-haired and drooling, while driving under the influence of the date-rape drug GHB in 2002.
Evening Standard, 30 Jun. 2005.
Students of English literature may recall a play by Nicolas Udall of about 1553 with the title Ralph Roister Doister, a comedy that featured the eponymous Ralph, a swaggering buffoon who thought he was irresistible to women. It features a letter to the virtuous widow whom Ralph is wooing, written for him by somebody else. Appropriately for a play written by the master of Westminster School for his pupils to perform, the script makes a teaching point: Ralph reads it aloud with the wrong punctuation, so that it comes out as a string of insults instead of flatteries.
Udall coined the epithet roister doister for him, based on the existing roister with the nonsensical rhyming doister added. Roister is an older form of the word that we would write today as roisterer, an extended version that entered the language when Sir Walter Scott wrote it that way in Abbotsford in 1820.