To pursue a teaching career in South Korea, you can indeed take a Korean language course at a Korean university, which will help you become proficient in the language and enhance your chances of securing a teaching job. With your IELTS certificate and a B.Ed from India, you could potentially become an English teacher in South Korea as well. For detailed guidance and assistance with your plans, Invicta Career Consultancy can provide valuable support in navigating these opportunities and ensuring you meet all requirements, While there are other options available, hence you can pay a visit to their website (icclearning.com) and get consult with them for better guidance. All the best to you.

Taking a Korean language course from a Korean university like SNU's Korean Language Education Center  can definitely strengthen your Korean language skills.  However, just completing a language course might not be enough to qualify as a Korean teacher in South Korea. Most schools require additional qualifications like:

You likely need a Korean Teacher's License, obtained through programs like SNU's Teacher Training Program or similar qualifications.

While not mandatory everywhere, a TEFL (Teaching English as a Foreign Language) certificate can demonstrate your teaching skills and make you a more competitive candidate.

An Indian B.Ed. degree with an IELTS certificate can make you eligible to teach English in South Korea through programs like the English Program in Korea (EPIK).

EPIK has specific requirements for applying, including:

• Bachelor's degree in any subject (from a recognized university)
• TEFL certificate (preferred)
• Native English speaker from a specific list of countries (including India)
• Clean criminal background check
  
  https://studyabroad.careers360.com/exams/ielts
  
  I hope it helps!