Dr Cunneen was a vet at the Redlands Veterinary Clinic, where five horses came down with the disease.
He spent five weeks in hospital, the last four in intensive care, before losing his life to the virus.
The service was held at Victoria Point, east of Brisbane.
The Australian Veterinary Association, in a statement issued the day of the service, paid tribute to a man they described as a valued colleague.
Dr Cunneen made a great contribution to the health and welfare of horses, its president, Dr Mark Lawrie said.
"Ben will be greatly missed. The thoughts of Australia's vets go out to his widow, family and friends," he said.
"We have been receiving messages of condolence from members since the announcement, and our close-knit profession feels Ben's loss very deeply.
"His colleagues at Redlands Veterinary Clinic will be hit very hard by this tragedy. Life has been extremely difficult for them since the crisis began, and to have this happen on top of all they've had to deal with will be devastating.
"We feel for all those connected to the clinic, and ask that the sadness they are feeling be respected at this very difficult time."