I would start by simply requesting it, passing along the psychologist's recommendation. Achievement test scores, if you have them or can request testing by the school (do they use the MAP or something similar?), would probably be more useful than IQ test scores alone. You could ask for her to take an end-of-grade test for first (or even second), depending on how advanced her skills are. Be polite but persistent in the face of claims about addressing her needs in first grade; there are helpful passages in "Developing Math Talent" about this being a poor approach, and you can hunt up other useful support for acceleration in "A Nation Deceived" and other resources.
Regarding whether she can handle the second grade work, I suppose that some areas of possible concern would be fluency, especially in math facts; ability to keep up with the handwriting load; and maturity level. These are all issues which could give an anti-acceleration teacher or admin support for a claim that the pullout wouldn't work, or wasn't working out after inception. On the other hand I wouldn't worry unnecessarily, as first grade math is typically pretty slow-paced. If possible, look up a scope and sequence for first and second grade math in your school or district, or requirements at the state level.
