who does she often help （to） do cleaning?这是针对her mother提问.
如果要针对helps her mother后面的do cleaning是宾语补足语也要去掉,就是针对谓语和宾语提问,应该是：
what does she often do?
如果按照题目要求可以变成：
what does she often do to do cleaning?句子的意思变了,to do cleaning由原来的宾语补足语成了目的状语,不能保持句子的原意,所以不成立,我估计最佳的答案是最上面,不过还是由你自己来做决定.