I have been very conscious in my reactions to wrong answers and imperfection and admit when I make mistakes and don't know things with a lighthearted chuckle and accept when she can remind me of something or finish my sentences and readily admit when I don't know something and we need to look it up online so she sees me accepting imperfection in myself.
I also try not to fixate on her being right or my being right. In fact when we disagree and she is completely wrong on something (she claims it is night not day at 8 am) I simply say, "You think it is night. I think it is day. We both think different things" and drop it because she will not be convinced of things if someone tries, so I just let her figure out what she can or we find another source for correct answers if she is interested since she hates backing down from a position she has taken even if she realizes she is wrong. If she is open, we could look something up in a book or on the computer.
I'm going to keep working on it being OK to not know, to be wrong, to make mistakes. When I was younger,I was very, very hard on myself. I remember literally crying when I got a 98% on a test (not IQ test, test in a class) as if that were a huge failure. I also cried when I received an A- on a paper. I have mellowed with age and experience and hope she can avoid that sort of inner pressure. It did not come from my parents since they had no interest in my school performance and didn't reward me for high grades. Really, my education and learning was all in my own hands.