Teach fingering to toddler

So we passed our first week of SM...

While we're making some progress (my 2.5 yo daughter now can recognise half of the notes - do, mi, sol and screams at the spiders), I realised that I don't know how to teach her the proper fingering. At the moment, she just presses/bangs the notes with the index finger although I showed her how to place the fingers.

My questions are:
1. Do I need to worry about it at this stage?
2. Will it come naturally once we progress further?
3. What was your experience?

Thanks heaps

I have a daughter exactly the same age, and with similar problems. While she recognises all the flashcard notes, and loves listening to the do-re-mi song over and over again, it is really hard to have her concentrate on the piano/keyboard itself. She obviously is still in the exploration state and merely slams the keyboard with her fingers. So far, "Can you show me Do?" and similar things shown in the videos have not been successful. She isn't interested in arranging the flashcards either, simply telling me that it's "not funny".

While she is fascinated by Mr. Oops and the spider in the Guess Key game, she won't press the corresponding keys when the notes fall.

Any advice or maybe similiar experiences? Will my daughter become interested in the piano if she sits on my lap while I play, or something like that?

I have to add that she is otherwise a smart girl. Brillkids' products have had a positive influence on her, and she reads very well, for instance. So I don't know what could be wrong. Maybe I should just give it a few months and hope for improvement?

Now, at last, things have started rolling! A few weeks ago, my daughter all of a sudden started playing Ode to Joy! This was the first piece she ever played, and I filmed it. (I will start a progress diary and upload the movie later on.) Ironically, she hated Mr. Oops, playing the Guess key game, and basically all other things proposed by you in the curriculum. But then I found out that she really loved the do-re-mi song from "Sound of Music". By now, she must have listened to it 300 times or so! Out of this, i.e. with the help of Julie Andrews, I finally managed to have her play the piano - and she was sure to start with her papa's favourite musical piece (except for Carmina Burana)!

By now, she is already playing the other pieces (Hot cross buns, French song etc.) quite well, but a new problem has appeared: the very topic of this thread. I am having the same problem as the thread starter here. During the last few weeks I must have tried everything in order to have her play with at least three fingers, but in vain. Showing her myself, trying to direct her fingers, showing your videos...nothing works. Even when I bribe her with ice cream she starts to cry when I ask her to play with three fingers. So what are parents having this problem supposed to do? As far as I understand, you are telling us that the problem will pass with age, as she enters a new stage in her development? But when exactly will this happen? Are we supposed to let her play Ode to joy, Hot cross buns and French song with her index finger every night for the next six months, or what?

In other words: Where am I supposed to go from here? How can I break this deadlock?