Reading your post reminded me of how much one of my sons LOVED the guitar at that age. We bought a cheap one for him, and he literally dragged it all over the house with him and played with it for months and months. It is in our family picture from his three year old birthday, as it went everywhere (in the house) with him at that age.

He was attending a music class then, and the instructor said that they couldn't teach children guitar until around five or six, because they just didn't have the correct hand size and strength. By the time he was five, he was no longer interested.