My first choice would be to use a centre lathe (as CHJ suggested). Catch the plate in the inside jaws of a three-jaw chuck, take the bulk out with successively larger drills, and finish by boring to a nice fit on the shaft.
If no lathe is available, and the pillar drill won't turn a 1" drill in steel, then there's a hand method that might work. Mark out the centre of the 150mm plate, and lightly centre-pop. Set a pair of dividers to 1/2", and scribe a circle using the centre pop to anchor one leg of the dividers. Lightly centre-pop round the circle at about 1/8" intervals (that's so that you can still see where the line was when you're nearly there - a circle of half-centre-pops is easier to see than a scribed line). Chain drill inside the line, using whatever size of drill the pillar drill will comfortably push into steel. Join up the holes by file to 'lose' the bit in the middle. Then, using a turnip half-round file, remove the bulk of the rest to near the line. Switch to a second-cut half-round file, and ease the fit until it almost goes onto the round bar. Then switch to a fine half-round file, and ease out the last few thous for a nice fit (interference, sliding or clearance, as desired) on the shaft.
May sound like a lot of work, but since it's only 1/4" plate, it won't be too bad, and you can control the fit between shaft and plate. You can't do that with a hole-saw, unless you 'saw' small and file to fit.
