Of Scottish origin, the colloquial phrase not to have a scooby, or not to have a scoobie, means to have no idea at all—synonyms: not to have a clue – not to have the foggiest.

In this phrase, scooby, or scoobie, is:
– short for Scooby Doo, the name of a cartoon dog which features in several U.S. television series and films;
– rhyming slang for clue—this, incidentally, shows that rhyming slang is not restricted to Cockney.

The earliest occurrences of the phrase that I have found are from articles published in The Herald (Glasgow, Lanarkshire, Scotland):

1: From an article titled The minister, the hotel chain, and a few personal reservations, by Jack McLean, published on 19^th April 1990—Ian Lang (born 1940) was the Minister of State for Industry and Education at the Scottish Office:

Mr Lang and all the other complacent worthies who make up the careers and education industry don’t have a scooby about how bloody awful it is to find yourself the recipient of grandiose schemes for ‘”training and industry” when it ends up with hardly much more in your pocket than you would get if you were to idle yourself away on the dole and not have to take snash [= abuse] from customers who have no intention of worrying about your wage, status, lifestyle, or anything else.

2: From an article titled No Headline Present, published on 14^th May 1993:

How would you feel if you jouked into your doctor’s surgery to find the chap asking you to park yer arse and gie us yer jackanory. Your lawyer telling youse that he husnae a scooby and youse can jist take a wee tirravie tae yersel. How would you go down at your interview if you didn’t jag your accent, dialect, Scots, up a wee notch?

3: From an article titled A great race run by women for women runners, published on 31^st May 1993:

The sun was splitting the skies on Saturday. Yesterday it put its hat on and it was a rotten trick. Was not yesterday when the first ever City of Glasgow women’s 10k race took place.
Now I don’t have a scooby what kilometres are (a colleague tells me right now that you divide by eight and multiply by five, but what you divide and multiply naebody seems to know) but it stretches from running them in 35 minutes as the winner, ex-Olympic athlete Lynne McIntyre did, to last runners who managed hours and were being picked up by Parks and Leisure Department cars all over the place, and didn’t mind.

The phrase occurs in the affirmative in Officially sanctioned thievery, published in The Herald (Glasgow, Lanarkshire, Scotland) of 9^th July 1993:

E. R. L. Fitzpaine. How to start a column. Anybody who has a scoobie what that august name wis and how so will have to be over 45. But once his name was legend. For every omnibus, tram, trolley, and letter heading of Glasgow Corpy Transport had ERL emblazoned upon themselves.
Fitzpayne was the boss of the Corpy and a name to be conjured with, a bit like H. Stewart Mackintosh of the Education Department. They had been in their posts so long you got to think that Winston Churchill was a fly-by-night.

I have found occurrences of the phrase in other Scottish newspapers. The following, for example, is from the column Jonathan Brocklebank on Wednesday: A personal look at what’s making the news, published in the Evening Express (Aberdeen, Aberdeenshire, Scotland) of 10^th April 1996:

The last waltz …
It was brought to my attention this week that some raw recruits in the RAF have no idea how to waltz or foxtrot.
Incredibly, it appears some feel most at home in these new discotheque places, wiggling their bodies like Elvis Presley to that thumping racket they call music these days.
Worse, some of those whippersnappers haven’t a scoobie about the correct form of address for Archbishops.
Naturally I couldn’t believe my ears when I heard the news. I thought someone was pulling my chain. But their superior officers have confirmed the horror story and sent the miserable lot of them on etiquette courses.