Can doctors test for food poisoning or do ers do it?

No specific test. There is no simple tests for common food poisioning; some tests are available but the treatmetn is usually symptomatic so these are not normally done...
Not sure of question. I don't understand your question. Are you asking who orders blood or stool tests for infections that may cause food poisoning? If so, that's doctors. I'm not sure why you split doctors from ers. The people who see you in the er are doctors too.