They are not wrong but they're not the most natural either.
여행하다 is a verb used in more formal contexts. And we say 한국을 여행하다 with 을/를 for this verb.
In day-to-day speech, we usually say (-에/으로) 여행(을) 가다.
So you can say it like these (personally, I think the two are equally clear and natural).
- 한국(에) 여행 가는 것을 좋아해요.
- 한국(에) 여행 가기를 좋아해요.