Nail Quarter Round To Floor Or Baseboard. Quarter round molding is a common choice for baseboard trim. It is inexpensive and simple to install.
For aesthetics, they both really should be installed together if the floor is not all In addition, the thickness of the new baseboard alone may not be enough to cover the required expansion gap along the new floor's perimeter; considering that. Also known as shoe or toe molding, it is used at the bottom of baseboards and cabinets to cover a small gap or uneven edge between the flooring and the baseboard. Better to use hardwood stained to match your laminate elsewhere or replace the carpet runner.
Sand the putty smooth and paint or varnish your baseboards.
In my house the quarter round was nearly half as tall as the base molding, which looked really silly.
I am also concerned about removing and replacing the baseboard. Go with new baseboards and forget the quarter round. Fill over the nail heads with wood putty and allow it to dry.