You could get testing if you can afford it. I am generally in favour of testing because it reassures you as the parent that you are not, in fact, crazy.
But you also need to think about what you want. She is already in the gifted programme - do you want her grade skipped as well? Or are you suggesting they differentiate (given the number of teacher's children that might not go down well), is there another programme in the district that is more selective?
The other kids in the class may or may not be gifted - I wouldn't advise mentioning that, but there is a big difference between 95 th percentile and 99.9+ percentile.
