Is graduation in English Honors sufficient for getting a good teaching job or should one opt for some post-graduation course?

With a simple Degree, we may not be able to go very far. There must be a PG also for a better understanding of the language and literature and for a better comprehension of books.

Dear, For getting good teaching job - undoubtedly M.A. in English after Honors in English in B.A. will give you an extra edge. Best wishes.