Is "I am not about this week" correct

We had an English test today and the correct answer to one question was "I am not about this week. I work in Romania" Is this correct and if yes what does it mean?

It's correct.

"To be about" is a common informal idiom in some forms of English for being in the vicinity understood from context (your workplace, your home, your home town, your normal haunts, etc). If someone will be about then while you may not be guaranteed to see them any given time it's a possibility. If someone isn't about then it's an impossibly.

I understand that the expression is more common in Britain and Ireland than elsewhere.