He was educated at Chester School and Trinity College Dublin, entered the King's Inns, and was called to the Bar 1808.
In 1830 he was appointed Chief Justice of the Irish Common Pleas, in which office he remained until his death from heart disease in 1850.
As Solicitor-General he is remembered mainly for prosecuting the 'Doneraile Conspiracy' case in 1829, and for his ferocious clashes with Daniel O'Connell, who appeared as defence counsel for several of the accused and secured their acquittals.
While O'Connell had a very poor opinion of Doherty (as he did of many of the Irish judges at the time, notably Thomas Lefroy), and treated his appointment as Chief Justice as a personal insult, most of his colleagues on the Bench admired Doherty's legal ability (though not a profound legal scholar, he had a great knowledge of Court procedures).
His courtroom manner was described as "theatrical and pompous", and his consciously "refined" accent made him an easy target for parody by opponents.