Though I am not a mom neither a Karate expert but I would still like to pitch in my view. In this 21st century you should not differentiate between boys and girls. Let your daughter go her way and do whatever she wants if she wants and is determined she can do any and everything.
All the best to both of you.

I agree
In addition girls should know self defense and for that martial arts is the best. SO, let your daughter take Karate classes.

My daughter is 9 years old and I am getting her trained in Taekwondo. I am very much into getting her self dependent and she should be able to defend herself in any situation and am sure this kind of martial arts training will help with the skills as well as self confidence.

Its definitely true that girls should have the skills of self defense but before that I would like to share my view on a child's liking. sixmiss, as you said your daughter is interested in learning Karate so why not let her go by her interest. We parents should not think twice before letting our kids go their way until and unless its something that is not reasonable or is harmful for the child.
If you suppress their liking for one time it may become a lifetime thing when she would not even speak up for what she wants or likes. So, just let your child do what she wants.

Karate is the best martial arts for self defense and as you said your daughter is interested it is always better to start at an early age when the kids have a flexible body. It is definitely strenuous in the beginning but slowly you child will enjoy it.