'월은 한자인데 달은 _____이에요'
My guess is that the intended meaning is: "월 is a hanja(한자) word while 달 is a native Koran word".
A better way to say it is: '월'은 한자어인데 '달'은 ___이에요.
(Strictly speaking, "a hanja-based word" should be expressed as 한자어, not just 한자).
The Korean word for "native Korean word" is 순우리말, or 고유어 as a second choice.
So we can say: '월'은 한자어인데 '달'은 순우리말이에요.
순우리말 is "순(pure) + 우리말(our word, our tongue/language)", where 순 is a prefix used to emphasize the nativeness. 순 is kind of necessary in this context because if we just say 우리말, the implication would be that 한자 is not part of Korean, which is not true.
우리말 is a common word by which Koreans refer to their language, together with 한국말. Just like 우리나라 (our country), it has the familiar "tribal" ring to it, and it's a Korean native word itself.
고유어 is a hanja word for "native tongue/language". It's used more often for languages of other nations.