I grew up doing martial arts. I had originally been put in at the age of 7 when my parents were trying to get me to learn the same things it sounds like you want your daughter to learn - confidence, focus, (I got a lot of it), etc. From the age of 7 until I went off to college, I attended True Martial Arts in Bellevue/Redmond (they also have a school on the Issaquah Plateau). It is a family-run school that has some of the best teachers in the area. They are extremely accommodating and very good with young kids. It took a few years, but I eventually learned all of the things my parents had hoped for, and so much more.
In terms of specific advice on choosing a school, the one thing I would suggest would be to visit a few different schools and watch an entire class before signing up. Talk with the teacher, talk with the owner, and talk to a student or two. Also, make sure that you are committed to taking your daughter for a number of years, as it is the setting and achieving of goals that makes martial arts so valuable.