I wouldn't keep your current quarter round if you are replacing the floors.

I am assuming that the new floors will be a different color.

If you want or need quarter round (or its cousin shoe moulding) after the new floors are installed, that is easy enough to do.

When my new hardwood floors were installed the flooring contractor installed new pre-primed quarter round in all of my rooms, except for the one room that had stained baseboards. For that room, I had to stain the quarter round, but the flooring contractor installed it.