What is normal belt progression?

I have a six year old who just started attending a local Karate school four months ago. I have some concerns .But, I must tell you I know nothing about Karate. Only what I have read on-line.
She attends twice a week. She earned her yellow belt her first month. And as I watch more classes I do not understand how it is decided when someone gets a test card. They gave her another card for her second belt test(orange)but I did not let her test for it yet. My reasons I felt where legitimate. She does not know here punches, or kicks, the ones she does know are done incorrectly. She does not even do her horse stance correctly half of the time.Do they grade children differently? Everyone seems to move from belt to belt very quickly! Adults and children. There are nine year olds walking around with black belts. Three kids tonight moved up to purple belts.Is this normal?I have coached for years and I always believed perfection before progression. Please let me know what you think. She loves the classes. But I do not want her to continue to attend classes repeating bad form. I feel it will be harder to correct the more she repeats the same incorrect moves. But I also do not want to insult the teacher if this is how they teach children.

Leeanna, Usually kids are not pushed as much as some one who is a little older. Usually starting about 10 they are pushed a lot. But under that they are grudually pushed up. Can i ask what style of karate your child is taking? That seems very fast to be getting a yellow belt the first month of training. I know that in our style it takes about 6 months to get to a yellow belt. Even to get to that the young students must be able to remember and perform techniques reasonably well for their age. In the end it will help her that you did not let her test, it will give her more time to perfect her form so by the time she is a black belt.. even if it is a young black belt, people everywhere will know she earned it and wasn't jsut given it. Sadly enough i have seen students like this. I have also seen white belts that perform better than the highest ranking in the class which are brown belts. There are also those instructors that teach for the money and dont really care what their students look like. Students should be a reflection of the sensei. Adults on the other hand are able to do more things and retain more knowledge so that may be why they also learn and advance soo fast as well. Usually an average time for someone to get their black belt is anywhere from 3-6 yrs (2 for tae kwon do.. sometimes)