Is there a possibility that she can skip later if the work seems inappropriate later on?

In our experience, dds both went into K reading at about the level you mention (they were both just shy of their 5th bds and just made the cut-off). In K, reading a grade or two above grade level coming in seems to be something they can accommodate and there isn't a lot of math beyond patterns, so it didn't drive even my more mathy kid nuts with repetition. The degree of mismatch btwn the curriculum and their skills became a greater problem later in elementary or in 1st grade. One of my girls became really miserable in 1st and the other stopped showing up except in body only. We've dealt successfully with my oldest -- the one who started melting down in 1st -- & she is a happy kid now. My youngest has ongoing issues related to not taking responsibility for herself and not being particularly engaged in learning. We're working on that still.

My girls may be MG or maybe moreso, but I'm not sure even though they have been IQ tested. They just have a lot of unevenness in their profiles so I am not sure if the composite scores fully reflect their strengths, but they may.

I am wondering where they got the 99th percentile from her WPPSI scores, though. 131 should be well within the 98th percentile range, which is still gifted, of course. Not that the one percentile will matter that much as it is within the range of test error and even a 98th percentile kid may need to skip a grade. My oldest, who was at 132 on the WISC (albeit with scores ranging from the 25th to 99.9th within one subtest), has successfully skipped a grade and it was probably a good idea in her instance. More highly gifted kids may wind up skipping more than one grade. Mine won't need that.