We have a similar issue with my older dd (7 y/o). She had no problems in kg and the teacher never mentioned anything. However, in first grade she had the teacher from h*ll who stressed my poor kiddo out until she was seriously depressed and we wound up taking her out to homeschool for the last few months.
It is the same thing that you describe -- she can do the work; she just doesn't do it quickly. For us, what has worked was having her privately assessed by a psychologist (IQ test, achievement test, self esteem inventory...). What we came up with was a child who hit the ceiling or came very close to the ceiling (as high as they could test) on all parts of the IQ test that were not related to speed. However, the parts that tested processing speed, she came in low-average (around 45%).
It has helped to have a very understanding teacher this year, but we are also in the process of pushing for a 504 plan for her (kind of a step down from an IEP) that will allow her to be given high level work, but less of it and/or be given more time. If she is given enough time, she can do work multiple grade levels above her current grade, but if she is pressured about time, she stresses out and works even more slowly. With an IEP or 504 plan in place, it kind of forces the teacher to comply with what your kid needs and not what s/he thinks dd ought to be able to do.
The conclusions that I have come to in relation to my dd's slower processing in relation to her ability are:
1) She has some sensory integration issues. We also had her evaluated by an OT at the recommendation of the psych and the OT found that she was sensory over responsive, which basically means that she is bothered by and distracted by sensory input that would not bother others. For instance, she was yelling at her sister for breathing too loudly in the car the other day. The fluorescent lights, the noise of the pencil scratching at the desk next to her... it all bothers her and makes it hard for her to keep her focus and get the work done quickly.
2) She is bored/lacks interest in the work. She not only needs harder work, she needs work that is qualitatively different -- more in depth, etc. She is a very compliant child and will do what is expected of her whether she wants to or not, but if it isn't engaging, she does it slowly b/c it is so uninteresting to her.
3) She has an unusual processing method that is not well suited to the manner in which children are taught in a classroom setting. Dd tends to observe things, think about them until she is sure that she knows how to do them right, and then she does them correctly with no practice. She is very easily humiliated and hates to practice anything b/c she sees it as making mistakes and having people see her do things wrong.
School is set up for the teachers to explain a concept and then have the kids do worksheets and so on to practice the concept until they know how to do it well. Dd doesn't do things that way. For instance, she learned to walk by watching others walk. She was mobile on the floor, but she
never pulled up on furniture, cruised around, or did anything that appeared to be practice walking. Then one day she stood up in the middle of the floor and walked all of the way across the room. Those were her first steps and she was then walking as if she had always done it -- no falling or stumbling like a new walker. She learned to read the same way -- almost nothing and then Harry Potter within a few months.
School is not set up for kids who are observers and contemplators, but if that is your child's personality, I firmly believe that the school needs to change and not the child. She is who she is and she should be learning how to capitalize on her strengths not have her personality pathologized.
I don't know if any of this applies to your child, or just mine

but I have found that the private assessments are very helpful b/c it is some objective "proof" of what dd needs, not just her mom saying it.