i took asiana airline from seoul (gimpo domestic airport) to jeju.. cost me abt 100,500+89,500won 2-ways (1998 prices).. slightly more expensive.. but iirc it's the only english website that sells korean domestic flights & there's a higher chance that the counter staff can speak english (just in case if i needed help during check-in).. paid using my citibank credit card.. coz the website requires payment by credit card that are "master secure"/"verified by visa".. i'm glad i chose asiana.. booking & check-in were easy & hassle-free.. they have flights from incheon to jeju & jeju to daegu too.. u can check them out here ->
http://www.flyasiana.com/english/