Well, since you are the parent, you need to take the lead in it.
Your daughter is just the way she is....there is nothing wrong with that.
But as her mom being the same way... it makes you uncomfortable because your feel you "have to" say something and talk away.
Maybe you don't 'have to.'
If you and she "connect" on another level.... then that is great! Not everyone connects, by talking. They connect in other ways.
So maybe that is her personality.
So you feel she is distant from you? Or do you think you and she have a good relationship??? Because, THAT to me, is the main issue..... do you and she have a good-positive relationship?
It doesn't matter how much or little chit-chat you make. It is the relationship you have with her... that she KNOWS she can trust you, that she can always come to you with any problems, that she knows she can come to you for a hug or encouragement, that she can come to you when or if she is scared or feeling down, that she can come to you for ANY reason under the sun, and that you WILL be there no matter what... without judgment. Just unconditional love.
THAT is the point.
Not how often you chit-chat or that you have to chit-chat every minute.
Or just ask her. That is what I would do. You are the parent, and she is only 8, and that is what Mom's do.
My daughter, can be like that sometimes... in certain moods... so I understand. But I can read her well... and I will just ask her stuff. I don't "fear" making her feel probed. If she feels that way she tells me. And then I say "I'm your Mom... I just care." Then she opens up.
And, being happy in silence is okay too. Not everyone can do that.
Maybe on your part, you can take classes or something... to develop your talking ability and comfort level. I know a woman is like how you describe yourself... but she made herself take "Toastmasters" classes and joined the club... just to improve herself. She has fun with her club.
All the best,
Susan