Under normal circumstances, I do not recommend home-schooling. Unless your kid suffers from some actual medical conditions (physical or psychological) that would make it difficult for him/her to mingle with a group of people (like maybe Down's), I would suggest getting your kid out to socialise. They need friends and an environment that fosters relationships. Academic achievements can never only be the sole considerations in considering a kid's education.

If you've no confidence in public education system, at the very least go for a private one. If it's too unaffordable, at least try public until standard 6. Then, decide what to do again when your kid completes primary education. One step at a time. I would not recommend home schooling.

My entire point was that the bolded sentences you wrote should not be the sole determinator of whether home-schooling should be opted over public schooling.