FSIQ and GAI are figured based upon rarity of scores. In my eldest's case, her GAI was about 3 percentiles higher than her FSIQ b/c that processing speed index really lowered her FSIQ.
A child who does as well as your dd on PRI and VCI is, apparently, in the top 3 out of 1000 as you note. A child who does as well as your dd over all four tests is less rare. I may not be making any sense...
GAI looks at the two indices that are most correlated with intellectual giftedness. Auditory short term memory and speed (which is part physical dexterity and part mental processing speed) are a part of intelligence, but not as much associated with "G" (the factor that is raw intelligence or giftedness) as are verbal and perceptual reasoning.
A child could have had the same four scores as your dd but mixed around btwn the indices, for instance, and still had the same FSIQ. So, say a hypothetical child got a 99.8 on PSI and a 94 on PRI (the flip-flop of your dd), he would still have a FSIQ of 138 like your dd. He, however, would likely appear very different, have more strengths in being quick, but not be as able in some of the areas that are associated with G -- like perceptual reasoning. For that reason, his GAI would be much lower than your dd's.
