When is the best time for a child to start learning the piano?

Many children start to learn piano (and violin) at aged 3 or 4. The Suzuki method is very popular: http://www.internationalsuzuki.org/method.htm . At that age, it is mostly 'play' and they are learning, basically, that there are high and low notes which correspond with notes that they sing. Just let her experiment with the keyboard at first to see what notes it makes. She will, no doubt, make horrible noises at first as well as nice sounds. If your keyboard is touch sensitive, she can practice making very, very quiet mousy sounds and big roaring lion ones. She can also learn to play a note and then to sing it. Let her experiment for herself and try not to guide her too much. Children can actually learn to read music before they learn to read words (music is much more logical than words!) but only begin to teach the musical stave when she begins to be curious about how you play a tune from music. At first, she will easily see how notes go up and down in a tune and a little later come to the concept of long notes and short ones. As long as playing music is always fun for her, you will be very surprised at how quickly she learns. Once she has a reasonable understanding of making a tune on the keyboard, you might begin to think of formal lessons (which will still be fun, of course).

If she's showing interest, then start looking for a teacher who will teach the very young. Not many of them will. My MIL has been teaching piano for almost 40 years, and she won't take anyone under 2nd grade. My best friend does group classes for kids starting at age 3-4. I am a music teacher myself, and I don't recommend Suzuki, for a myriad of reasons I won't get into here. If you have some musical knowledge yourself, you can check out some of the programs for the very young, like Music for Little Mozarts - there are great exercises in there to get them started.

Morning, sunny. I think that it is a good start for you to play the piano while your baby sings to the songs you play to help her with some sense of music and the beat to the songs you play. When she has already developed a very good sense of music, then it is time for her to learn to play it herself. It won't be long before she learns how. You know, kids nowadays are much cleverer than the time we used to be as they see more things...

As soon as she wants to learn. If she already shows an interest in it, then you can teach her the basics right now. If she keeps wanting to learn more, then keep teaching her. If you've taught her everything you know, then get her a teacher. I don't think 3 is too early to learn to play the piano.

as soon as she is able to start tapping keys, we take a lot more information in as babies, my middle one is 3 and she knows the difference on her electronic organ of the keys and can make rhythms but I started her when she was 2 lol, just messing about on piano's and electric organs. So the younger the better, its only us adults that seem to struggle learning new things sometimes, its like my eldest we go to spain on holidays 3/4 times a year and my eldest can speak spanish at the age of 6.

I think if she is showing an interest in it then now is when she should start learning. Little ones are like giant sponges that soak up everything we put into them, they have no fear of failure and a joy for accomplishments rarely enjoyed by adults. The more fun it is, the more willing they are to learn.