It should be like this:
"Are you going to hospital?"
"Do you go to hospital?"
"Are you going to hospital?" means you're asking someone whether he/ she is going to hospital now (in present or in the nearest future)
"Do you go to hospital?" means you're asking someone whether he/ she goes to hospital regularly (a habitual action)
An example:
"Do you smoke?" means you're asking a person if he has the habit of smoking.
"Are you smoking?" means whether the person is smoking now.
