umbilical cord falling off on pieces

So my little girl is 3 weeks old today and about 10 days ago majority of her umbilical cord fell off. However the "stump" part that was inside her belly button still is there (see photo). I called her pediatrician when the original piece came off and she said to just apply alcohol to it and it will help it dry up. However. It is still there. I touch it gently and it doesn't appear to be getting any looser. It doesn't cause my daughter pain. I'm just unsure what to do in this situation. I was thinking if it's still there by Thursday or Friday I'll take her to her pediatrician. But even then I don't know if there is anything she can do. Any advise is appreciated b