Your husband needs to hang around a typical nursery school to see what average really is. Or print and show him a typical milestone development chart.
There is no way that any of what you are describing is normal. Of course the fact that most people marry someone close to their intellectual ability (shown or hidden) and that therefore their children are generally similar in intellect to them may also help him accept that she is not average at all. Not even on the gifted continuum I would hesitantly say.
You are doing great to keep going according to her interests and readiness, so just keep doing that. Let her explore and learn on her own, and just keep having interesting stuff around for her to figure out from. She sounds delightful and self-motivated which is a great combination! Provide her with an interesting environment and trust that she will do what she needs right now. Exploring and experimenting on their own is not bad - it has merit, in that it creates the ability and desire to self-teach, which in the long run will make your life a LOT easier, esp if you decide to homeschool / unschool
