My old flooring has quarter round trim at baseboards. I want to install laminate flooring over old, do I HAVE to take up the quarter round? Is there some other trim that can go on the new flooring edges that butts up to the existing quarter round?
No. Rip up the old quarter round. If you cannot get it up without damaging it, then just replace it. The laminate flooring should extend to about 1/4 of the wall, and that gap is covered by the quarter round. You do not want multiple runs of quarter round going around the room that would be just plain silly.
The proper way to do this is to remove the existing quarter round, then install your new floor. It's imperative to do this if the new floor is a floating floor since it will need room to expand and contract. When re-installing the quarter round do not nail the quarter round to the flooring or pinch it too tightly. Floating floors have to have wiggle room otherwise it will buckle up somewhere.
Gently pry up the quarter round with a pry bar and mark it with tape as to where it goes. After you put your floor down you can put it back in place with a few finish nails. It sounds like a pain but it is the proper way to do your floor and cover the edges of the laminate. It will add a little more time to your project, but the results will be well worth it.