Hi sunnyhope,
it sounds like you already started on the rail fence. Why don't you want to finish it? Just because the baby is already here does not mean that you can't give the gift later. After all, the little one will not be able to recognize a quilt for a while (and she won't miss not having one.)
This quilt is important for your skill development. I think you will learn a lot just finishing the rail fence. It is a lovely baby pattern and appropriate for a beginning quilter. Nobody will (or should) look at your gift and criticize you for having chosen that pattern. I am sure that a well-done rail fence will be loved and appreciated by the recipient.
My recommendation for you is to stick with it. Finishing feels soooooo good (trust me, I know all about that).
Happy quilting.