What qualifications do I need to teach English in Vienna?

Dear All, I am a qualified teacher of English as a Foreign Language/ English as a Second Language from Hungary. However, I am not sure at all, whether I am allowed to apply for English teaching vacancies in Austria (Vienna), or not. I have an MA (university) degree in teaching English language and literature - I am a philologist. I graduated at a Hungarian institution. I have seven years of practice in teaching in public schools and 17 years of experience in private teaching, and in language exam preparations. Shall I take any international teachers' exams before applying? In Austria, I wolud like to teach either in a public or in an international school. Can anyone help me by providing relevant and trustworthy information on this subject? Kind regards, Gabor