Thing about Dowun is, he's creepy, but he's also currently her best chance of a life where she isn't constantly insulted, belittled and stepped on, where she'll have a chance to learn and improve herself and get some respect. Sooner or later she'd have ended up a maid, or thrown out of the palace. Sure, he's not offering romance, but he's offering quite a bit, and what has romance ever done for her? And who in her social milieu ever marries for love? We can worry about following her heart and stuff because we have the luxury to.
This is a story, so she'll end up getting it all, romance and the whole nine yards. But if it was real life, she'd go with it and it would be, if imperfect, still the best and most important decision she ever made.