This seems to be one of, if not the most popular forms of home education in the UK: child-centred or child-led learning – an unstructured learning approach which allows children to pursue their own interests. I would recommend reading books by John Holt and Patrick Farenga. Check your library first.
One of the reasons families decide to educate their children at home is that they feel that formal schooling starts too early. This is borne out by research undertaken by US educators Dr Raymond Moore and his wife Dorothy. Unsurprisingly, the US school system wasn’t receptive to their research, and they have since become advocates of home education and written several books.
The Moores advocate learning good habits, helping with housework etc. in place of early formal learning, whereas in the UK, the focus would be on natural learning through play.