My feelings on this are that a skip is likely to help, even if the skip is not all the way to the level where your child could be working.
Some things to consider:
It is easier for a teacher to differentiate up one or two grades than it is to differentiate up three or four.
There is a much greater chance that there will be other students working at a fourth or fifth grade level in a third grade class than in a second grade class.
If your child has difficulty finding age peers who share interests, moving ahead may improve that and therefore improve the overall school experience even if the academic level and pace is still not quite right.
The larger the skip, the more likely that expectations for handwriting and organization will be developmentally inappropriate.
There is nothing stopping you from asking for another skip later if it still seems indicated.
