One thing that you may want to look at is the curriculum requirements for second grade. When I did this and compared them to first grade, there were few differences.

Another tool you can use is the IOWA acceleration scale. Ask your school if they have one.

130 is a gifted IQ score, 145 is often considered highly gifted. The psychologist should have explained to you that the GAI score is more indicative of your daughter's abilities than the FSIQ.