sam11,
Your DC has very nice test scores, with good consistency within the index areas. None of them are really low; even the relative weaknesses are all solidly Average. The strength area, at the top of the High Average range, is in verbal ability, which usually bodes well for academic achievement. I will note that the WISC-IV is an older test, which has since been superceded by the WISC-V, released a little over two years ago. This may result in slightly high estimates of ability, due to norm obsolescence (aka, the Flynn effect). indigo has already mentioned that his extreme youth also suggests interpreting scores with caution. Bottom line, though, is that this is a capable child, especially in language.
Regarding your concerns with inattention, impulsivity/poor self-regulation, and high levels of activity, these are indeed often considered the hallmarks of ADHD. They are, of course, also characteristic of many neurotypical six-year-olds, especially in certain settings. The WISC data you have provided is not really sufficient to establish whether some kind of distinct learning profile is responsible for the behaviors. True, those diagnosed with ADHD not uncommonly have relative weaknesses in WMI, PSI, or both, but there are many people with relative weaknesses in those indices who are not at all ADHD or otherwise learning disabled, and appear to have no marked functional challenges.
If your DC's behavioral presentation in the classroom is a cause for ongoing functional concern to you, the teacher, or your child, then it may be worthwhile pursuing a more comprehensive evaluation, perhaps including rating scales and direct measures of attention and executive function, and academic achievement, such as those conducted through the public schools by a school psychologist, or through a clinic or hospital (possibly through your insurance) by a clinical or neuro psychologist. The data you have currently, as valuable as it is, is really insufficient to "explain the behaviors".
As a side note, if your DC does have a neurologically-based disorder of attention for which stimulant medication turns out to be appropriate and effective, it may be that testing results will look different (likely higher) under medicated conditions. As a little plus, since the examiner gave an outdated test, if a re-test on meds became indicated, the WISC-V would be an allowable instrument. (Normally, 24 months wait time is required between administrations of the same test.)
