In my local medical clinic it's the Dr. who gives the injection. Most other vaccinations are administered by nursing staff who are qualified.
The turn over of patients is quite quick so someone must be making quite a few dollars doing this simple task.
Maybe I'm a bit cynical but why only the Dr. and not the usual nurses? As a previous poster put it " maybe a money spinner " here!!
Anyway the quicker it's done the sooner we can get everyone vaccinated and try to return to some sort of normalcy.