this word doesn't come from anything to do with the dole or unemployment, it's a north-eastern english word originating from the mining community's use of different types of lamp whilst 'doon the pit'. An early, dangerous lamp nicknamed the Scotch Davy ('Divvie') had a high propensity to explode, and was superseded by safer lamps such as the George Stephenson ('Geordie') lamp. So someone would be unwise to go down a mine with a Davy/Divvie lamp, hence the word coming to mean a daft or silly person. Non-offensive and can be affectionate.
'Ye keep way from me if ye usin a divvy!' (Miners' usage)
'Ha, you're such a divvy' or 'He's a right div.' (Modern usage)