If your daughter is in school, the school district must pay for the assessment. At the age of six, I believe she would fall under the Early Childhood Special Education umbrella. They don't service children for Learning Disabilities at that age, but focus more on Developemental Delays (not reaching major miles stones). Once your daughter turns seven, she should be able to be tested for a learning disability by a school psychologist.
The definition of a learning disability (LD) used by schools in Minnesota states that a child with an LD experiences a discrepancy between their ability (IQ) and their achievement in reading, writing, and math (I think there are actually seven areas in which to qualify. Reading, writing and math are just the basics).
Before testing can be done, the school must document at least two interventions in which they have tried to meet your daughters needs. If these do not provided progress, testing for an LD can be planned. In order to prove a discrepancy exists the school psychologist or special education teacher will give your daughter a series of tests. The first of these tests deal with IQ. The second round of tests will look at acheivement. The Woodcock-Johnson is the test that is usually used in this second area. Very little is required to pass this test, which makes it difficult to prove a learning disability exists. Once these standardized tests are completed, scores from the two will need to be compared. If a child receives a 100 on the IQ test, they should receive a similar score on the achievement test.
It's important to remember that you are an integral part of this process. You are your child's best advocate. I hope this answered some of your questions. Best of luck.