At the moment in Italy things aren't brilliant and there are less jobs than there were, say, 10 years ago. That's not to say that there isn't work, but you will have to be in the right place to find it. I wouldn't recommend taking a course with an organisation who guarantees work for you. With the degree that's fine (and of course the citizenship which will be required) but almost any TEFL certificate will do; at the moment in Italy it's not so much the qualifications you have but being in the right place at the right time, knowing the right people and also knowing Italian will help.