we are in the process of having DD8 evaluated by a private psychologist with a similar background, lots of experience with our district, etc due to 3+ years on noncompliance on my DD's part. She had an IQ test at 2.5 and the district's use of a test called the Raven are in agreement that she is at least 2 deviations above normal, so this is well within what both most schools and private psycholigists, etc term as "gifted"...but gifted does also have ranges...and it's relative. If your DD really DOES have dyslexia, I would think either of the testers you are considering should be able to find that. If you are expressing concern about that to the private tester, she should be explaining to you how the tests are used to diagnose and treat, etc...
On the other hand, it would be irresponsible of her to NOT mention (probably to all her clients) that sometimes the test shows the child isn't truly gifted, but still of above average intelligence
Your DD might also not have dyslexia, but something else...a well qualified evaluator should be able to unearth that. And that's not cheap either...answers cost money. Luckily, DH and I agree on how important this is and it's effect on our home life is worth what it will cost for us to get a better picture of what our DD truly needs.