"She went to learn Chinese in Taiwan later."
Put 'later' at the beginning of the sentence instead the end, that should make it clearer.
I believe that when you say 学习, 习 is actually the object of the verb 学. When you specify what you are studying (中文 in this case), that becomes the object of the verb 学. So you can 学习 (study) or you can 学中文 (study Chinese), but I don't think you can *学习中文.
Because Duolingo is in the midst of refining this course. At any rate, 学 sounds smoother and is the better choice here.