Hello,
The only qualifications you need to get a job in Korea is a university with some field related to English.
It sounds like your degree would be fine.
The starting pay is usually around $2000 a month, you will be provided a furnished apartment (usually small) and a round trip airfare (half on arrival, half on completion of a 1 year contract).
If you check out some ESL jon boards you will get all the info you're looking for.
A lot of people become ESL teachers with zero teaching experience and no CELTA/TEFL qualifiation.
I would recommend doing a course before though cos it makes it so much easier when you find yourself in a classroom.
It is a relatively easy profession to join.
Hope you enjoy it!