A man has been charged with murder for allegedly deliberately striking a doctor he knew with his car in a "spur of the moment" hit and run in Brisbane, police say.

Key points: Dr Dunne was jogging in Tarragindi, in Brisbane's south, about 4:00am when he was struck

Dr Dunne was jogging in Tarragindi, in Brisbane's south, about 4:00am when he was struck He fought for his life in hospital for six weeks

He fought for his life in hospital for six weeks Police say a local man charged with murder knew the victim

Brisbane GP Peter Dunne, 53, was on his usual early morning jog six weeks ago in Tarragindi when he was struck.

He was found on the roadside about 4:00am with critical head injuries, and died in hospital on Sunday.

Police arrested a 32-year-old Tarragindi man yesterday.

Detective Inspector Mark Thompson said it will be alleged the defendant recognised Dr Dunne as he was driving past.

"We will be alleging that one of those vehicles turned around and turned back to where our victim was and deliberately aimed his motor vehicle at the victim and ran him down," he said.

Police have been appealing for witnesses and released CCTV footage. ( Supplied: Queensland Police Service )

"I don't believe it was a planned incident.

"I would suggest, to put it into basic terms, it was just a spur of the moment turnaround, and [he] committed the act.

"We believe that the two males have crossed paths in the past."

Detective Inspector Thompson said Dr Dunne's family were extremely traumatised.

"[He was] a well-respected pillar of the community," he said.

"His last days were decided upon by somebody else, now that's a tragedy in anyone's mind."

The matter was heard in the Brisbane Magistrates Court this morning and was adjourned until April 29.