Two thoughts: not all kids will have the mental development or fine motor skills to learn to read or write at three. A few kids don't get there till closer to third grade. They generally have other skills that are much stronger that other children, though, and those early readers may take a few years to catch up in those areas. So don't assume that all 3-4yo's can succeed uniformly with enough work, and give her lots of leeway so she doesn't end up feeling a failure before she has a chance to get there.
Also, I don't think that most kids learn to hold an instrument or write by copying someone else. If that seems helpful to your daughter, you might try setting up a mirror on your table so she can watch your actions in reverse. Or sit across from her, instead of beside her.
But what she will probably get the most gain from would be just manipulating stuff. Clay, crayons, pencils, paintbrushes, making simple drawings for the sheer joy of it, and identifying shapes from books and pictures. She may be able to name shapes or even letters long before she can write them, just as people learning a foreign language may be able to decipher words and phrases audibly long before they can start stringing them together verbally.
Reading and writing are tools that are there to serve us when we are ready. When that time comes, they are wonderful. But we shouldn't make our children slaves to the tools. Your daughter will get there when she's able, and not a week sooner.