When a child asks to be homeschooled for reasons other than lazy fantasies of studying in bed in pyjamas, he/she will likely thrive in that environment.

I was also homeschooled from K1-High School (not that common in Singapore, but since I'm in the network, I know of at least a hundred others like me there)..It was a great opportunity for me because you as a homeschooler can literally control your schedule. I was able to work as many as 3 part time jobs simultaneously while being homeschooled because of this, and gained lots of experiences and built my network of friends that way.

That said, if your daughter is more of an introverted personality, it might be useful to send her for other classes like dance, language, sports, etc so she can be exposed to and interact with more people. I come from a family of six kids - all homeschooled..and a couple of my siblings are very introverted, and they would have benefited a lot from some structured situations that forced them to build some social skills earlier on. I'm a mixture of intro- and extro-verted, so I found my way more quickly. There were some painfully embarrassing situations at the start of university though..

Anw, I'm really glad your daughter is doing far better now. She sounds like the driven, introspective sort..which is great...she should join steemit too ;)