Each S.D. should have its own rules regarding early entrance. In some SD it is flat out impossible, no way around it. Others have clear policies that might consist of a combination of factors: only a few months younger than required, some measure of IQ and achievement, social readiness, physical screenings (like skipping, balancing), etc.
I would look at your SD and see what their policies and programs are for gifted kids.
Skipping K might be good for some gifted kids, but it is not a good idea for others. Frequently K teachers are more used to differentiating since they can get kids not knowing letters and others already reading, same for other items. K can be more fun and open ended while 1st can be very rigid. In those instances, skipping 1st might be a better option.
an IQ test will not involve any reading or math (that would be achievement testing).
You can't have her repeat the test, because it loses validity. Many recommend waiting at least 1 year between tests, others even more.
A good tester should give her time and make her feel comfortable answering questions. I know many shy kids who did great on testing if the tester respects them and gives them some time.
I think that in many cases, testing as close as possible to Kindergarten entry as possible is a good idea. In some cases, it has to be done earlier to go with the early entrance procedures or private school's deadlines. The summer before entry could be a good time, you'd then set up a meeting to discuss results with the principal before class assignments are made. But, many principals are not even open to that.
