한국어를 말해요 is correct, because 한국어 is Korean language, whereas 한국 is Korea as in country. As an aside, your second sentence has 자는 instead of 저는 and if you were to attach 한국 to a verb via the object particle 을/를, it would be 한국을 because 한국 ends in a consonant. But I don't think it would come up, as 한국 is a place so I can't see you needing to attach it to anything with 을/를.

Koreans would say 전 한국말 할줄 알아요.