Den, you will find a lot of different answers to that question here. A lot of the reasons depend on how you want the area to look and the architectural style of the house. I have a 35 year old ranch with plain base mold but no quarter round. The carpet just goes up next to the base mold and stops. It fits this design. My daughter has a 150 year old farmhouse with big, wide moldings and quarter round. I would suggest leaving those in place. Another regular poster has plain moldings and quarter round with the quarter round elevated so the carpet end under the quarter round. That works for him in his house but you have to get with your carpet layer to find out how much to elevate the quarter round or paint it and then install it after the carpet is in.
I suggest that you meet with the design committee and determine what looks best in your situation. It may help to have a carpet sample, base mold sample and a piece of quarter round to help you visualize how it will look.