추다 is a transitive verb normally requiring an object. So i언니가 추고 있어요 sounds unnatural (although it's okay, if it's said in response to a phrase mentioning 춤을 추다).
춤을 추다 is very similar to 테니스를 치다. The fact that 추다 comes from the same origin as 춤 makes little difference grammatically.
Also note there is 춤추다 which is a short form of 춤을 추다.
In simple contexts, 춤추다 is usually preferred; but 춤을 추다 is sometimes the only choice because of a modifier, as in 새로운 춤을 추다, "do a new dance" (새로운 춤추다 is ungrammatical, as the adjective 새로운 requires a noun - only 춤을 추다 provides this noun).
영희: 영숙 씨는 춤(을) 잘 추세요? (adverb 잘 attaches to the verb closely, between 춤을 and 추다)
영숙: 저는 (춤을) 추어 본 적이 거의 없어요. (추다 without 춤을 is okay because it was just mentioned)
영희: 그래요? 춤 한번 배워 보세요. 춤추는 거 재밌어요. (No modifier, so 춤추다 is good enough)
So your original sentence is most commonly said as 언니가 춤추고 있어요. 언니가 춤을 추고 있어요 is about as natural, but 언니가 추고 있어요 is unnatural except in some special contexts.