My old house had white baseboards with oak floors but the wood went under the molding since it was original. I think all quarter rounds should be the color/stain of the floor.

but you want to keep trim/moulding around the room and doors in oak? They would look better white (to even out the baseboards)

I guess it all depends on how big room is, how many doors/windows....and how much time you have on your hands to paint :)
If you really want to keep the doors oak, then you should leave all else alone. keep it simple with all oak.
The white only baseboard will POP big time unless you have WHITE walls,ceilings,furniture.....

Most of the houses that I've seen with a mix of painted and wood surfaces have all the trim painted--baseboards, window trim, crown molding, and the trim around the doors. Then the floors and doors are left plain wood. Or one side of a door might be painted to match the decor in a particular room.

What style home is this? If this is a Craftsman with nice oak trim, it's pretty much heresy to paint any of it. You won't get wood overload if the floors are a different shade than the trim. Try a browner and slightly darker color on the floors.