Hi Padboz,
I have two girls, one is 3 in June, youngest, the eldest is 6 in July.
Bi, my oldest was very similar to your child in that songs, counting, colouring, drawing and especially talking were very very advanced compared to children the same age. She also had very good social skills. This darling has gone on to be the top of her class in Transition (Prep/Kindergarten) Year before grade 1. And is working at the level of a grade 2 or 3 in things like reading and writing. She also still has amazing social skills.
My number 2, Mol, is showing all of the same signs, and I can tick off against your list very easily. Unlike her sister, she is also very kinaesthetic, in that she dances when music comes on and doesn't realise she is doing it. She jumps and balances amazingly.
The difference between the two is my attitude. I know that Bi (5.5yo) has done well with attention and love and I will keep going with both of them the way I have in the past. I push them to try new things, but never force them to do something they dont enjoy more than once. This has worked for me and they are both turning out well.
As others have said, just enjoy her at 2 because trust me, she will grow up soon and you will wish she was two again. Like I did today when my 5 year old screamed in my face that she didn't know what to tidy up!
I hope this helps, I know how hard it can be to find information on these subjects, even when they are doing well academically at an older age.
Enough said!
ConniJ