The existing baseboards I assume are the kind that are flat, and you had carpeting there. I just laminated my whole upstairs to the house.
Ideally, you would remove the existing flooring (unless it's vinyl or hardwood). Once that is done, take your quater round off - not the "flat" baseboard that is there. If the "flat" baseboard is not already there, you can buy some that would act as both "flat" baseboard and quater round to cover the gap.
Install the new laminate flooring, and take the opportunity to clean and screw in the floor now to fix any squeaks.
Get an undercutting tool to undercut the door jambs for a more professional look. Nobody told me this and I did not undercut the door jambs. It looks ok but a little unusual!
YOU MUST leave a 1/4" gap between the laminate and the wall (or "flat" floor trim). It will expand and contract.. believe me!
Then, install the quarter round. It will look very good after is has been painted. Get caulking in case you need to touch up any cuts... using painter's tape and your finger, good caulking and paint will cover up any mistake.
When installing the quarter round, drill a small hole. If you don't, your nails may crack the quarter round. Also, I believe 2.5" nail should do it, to attach the quarter round to the current "flat" trim.