At the moment she must have played with him.这句话对吗？

不对。must have done是对过去的事情较为肯定的猜测，而at the moment是典型的现在进行时的时间状语。

At the moment 在目前
must have done 表示对过去的猜测 一般翻译为“当时必然在做某事”
时间上不一致
改为At that moment she must have played with him.