"You don't need to introduce us. I know her."
We can say 介绍 A 给 B to give this meaning. However, when saying it on the spot, both objects A and B are usually not mentioned.
我来介绍 Let me introduce (we don't say let me introduce you to him or him to you)
I think it is also very rare for A or B to say something like Please introduce me, me to A, or Please introduce B, B to me at the time they meet.
"不用" isn't currently accepted. Am I right that it's fine in place of "不需要"? If so, is there any difference in meaning?
I would like to make a complementary comment. 不用 is more instructive and 不需要 is a relatively subjective description about not having the need to do something.
You don't need to come (to work) tomorrow. You are fired.
You don't need to come to help me tomorrow. I can manage it by myself.