There are so many many things to consider when it comes to skipping a grade.
We all want our children to enjoy learning and being in a situation where everything is too easy is not a great start to enjoying the learning experience.
I’m talking from personal experience here as my parents decided that extra curricula activities would be of more benefit than skipping a grade or two at school. In many ways their decision worked out fantastically - I have many many skills in areas I am passionate about and the only reason I was able to do all of these is because school was so easy for me.
Having said that I never had any respect for education - in the school sense. It bored me senseless I felt I could do it all in a quarter of the time myself and have more time for more important things. Self education and my extra curricula activities were met with extreme discipline, stick-to-it-iveness, joy, passion and appreciativeness of the opportunity.
I hated, even dreaded, school. I had trouble conversing with the kids in my classes and by high school was tending to hang out with much older children and even teachers. My social skills suffered as a direct result of having no one in my classes who enjoyed what I enjoyed or understood what I understood. I played up in class and was almost constantly in trouble until I finally swapped to the public school system and was put into the gifted and talented and talent development programs. Unfortunately I was well into highschool by this point and never really learned to enjoy the classroom.
Had I been put ahead academically to a level that would have challenged me and with kids who were thinking at the same level as me I may have enjoyed school a lot more and had less trouble socialising as I grew up. I still would have coped with the extra curricula because I was naturally bright.
I believe if you are truly gifted (not just well coached and tutored) then you need to be with other children who think at your level.
So the things to consider, I guess, come down to what you know of your child…are they ahead because you have done amazing things and given them a great educational headstart or is he also thinking at a level above his age? Reasoning skills and conversation levels and imagination levels are all things you should take into account.
He does read and write well and does maths well but how are his gross motor skills? Did you also do the physically superb program? What kids does he like to play with children his own age or older children? Is he a leader or a follower - personally I would be reticent to put a follower ahead I’d let their achievement levels that will come from being ahead help them gain confidence and learn leadership skills. However if they naturally play and converse well and hold their own with older children then put them ahead in a place where they will be with children at their level.
Another thing to consider is when they skip a grade. Better sooner than later. Skipping kindy or year one is one thing but skipping year 8 is another. I’ve seen talented dancers skip grades and as a result end up with patchy dance education because every grade in the syllabus is designed to teach the foundations for the following grade. It is the same in school curricula. A friend’s brother skipped year 8 because he was talented but had as a result not been taught some of the work that you needed to know before your learned the year nine work so he ended up having to do double the work sometimes to fill in the gaps. Far better I think that they work at the right level from the beginning. Being able to cope cognitively with the concepts of the work is not the same as having good foundations laid for doing the work.
Good luck with it 
He is also writing at a level beyond his years and LOVES doing simple addition and subtractions.
I wish you all the best in your journey …