He was educated at Winchester College and at Christ Church, University of Oxford and then chose a military life. He served in two campaigns under the Earl of Stair and three campaigns under the king of Sardinia, where at the siege of Coni, he distinguished himself so much that Charles Emmanuel, King of Sardinia, ordered his ambassador in London to wait on the Duke of Queensberry to thank him for the services performed by his son.
He married on 24 July 1754 Lady Elizabeth Hope, daughter of John Hope, 2nd Earl of Hopetoun, but accidentally killed himself near Bawtrey, in Yorkshire on 19 October 1754. Lady Drumlanrig died only 18 months later.
Henry's brother, Charles, succeeded him, but died in 1756, leaving their father without heirs. The Queensberry titles passed in 1778 to a distant cousin, William Douglas, Earl of March and Ruglan.
- "(44) - Drumlanrig Castle and the Douglases -Histories of Scottish families -National Library of Scotland". digital.nls.uk. Retrieved 2018-09-18.
- "The peerage of Scotland: containing an historical and genealogical account of the nobility of that kingdom, ... collected from the public records, and ancient chartularies of this nation, ... Illustrated with copper-plates. By Robert Douglas, Esq;". quod.lib.umich.edu. Retrieved 2018-09-18.
- "Person Page". thepeerage.com. Retrieved 2018-09-18.