'As queen' is correct. You don't use an article here because there is only one queen relevant to the story, or the country in question. Same with 'As president of the USA...' or 'As ruler of Surinam...'
You'd say 'as a...' when there are lots of possible instances of the type of person. For example, 'As a doctor, you sometimes have to make difficult decisions' (there are lots of doctors). Or 'As a mother of a young baby, you don't often have time to rest' (there are lots of mothers).