Wordorigins.org

Dope has a variety of meanings, most relating to thick, viscous liquids. It is an Americanism, coming from the Dutch doop, meaning sauce.

It first appears in the writings of Washington Irving from 1807, in a sense meaning sauce or gravy:

Philo Dripping-pan was remarkable for his...love of what the Dutch call doup.

This sense expands in subsequent decades to encompass a number of thick, syrupy liquids used for a variety of purposes.

Towards the end of the 19th century, dope was being used to refer to illicit drugs, specifically opiates, because of the viscous qualities of opium that has been prepared for smoking. This sense appears in a 2 May 1888 headline in the Los Angeles Times (too bad they don’t write headlines like this one anymore:

“Dope" Fiends. Police Officers Raid A Notorious Den. A Sallow-faced Pipe-hitter and a Nude Female Captured—A Disgrace to Civilized Los Angeles—The Unfortunate Girl Weeps Bitter Tears.

Dope, as applied to horses on the racing circuit appears a bit later than the opium sense. From Cullen’s Chances of 1898-1900:

Dope makes a horse about as frisky as three drinks of whisky makes a man who’s been off booze for a long while.

This horseracing sense apparently gave rise to the sense of dope meaning information. Knowing which horses had or had not been doped was critical information for gamblers. From A.H. Lewis’s 1899 Sandburrs:

Mike is an oldtime tout...an’ we’re runnin’ over d’ dope in d’ papers seein’ what d’ horses has done.

Moving to more recent years, the adjectival sense of dope meaning excellent also apparently comes from the drug sense, in this case from the quality of the high given by heroin. This sense arose in rap music circles in the early 1980s. From Stanley’s 1981 Rap:

Yo, man, them boys is dope...This record is dope.

The sense meaning a fool or idiot appears in the mid-19th century and it may be unrelated to, although it certainly was influenced by, the drug sense. It appears about the same time in both Britain and the U.S., and these two usages may have arisen from different sources. The early British uses, in particular, may be etymologically unrelated to the other senses of dope given here.

Dope is defined as a simpleton in an 1851 glossary of words found in the Cumberland dialect. And E. Lynn Linton, a writer from Cumberland, writes in the 1866 Lizzie Lorton of Greyrigg:

A “downo-canno dope"—which meant a spiritless simpleton.

On the left side of the pond, the Journal of the Illinois Historical Society records the following usage from 1862:

Kersting came in his stead, a nice well educated man, but a dope.

(Sources: Oxford English Dictionary, 2nd Edition; Historical Dictionary of American Slang)