I don't have any idea what size ya need,
But I'm sure ya can buy some steel rod that is at least very close in size and then turn it down to the proper size, although I don't have a lathe I have been able to size small stuff like that by chucking it up in the drill press and using emory cloth to cut it down to size. Yes the brass may act as a lubricant,but many many carbs had/have steel shafts & cast bases using no bushhings, tolorence needs to be fairly tight so ya don't have vacume leaks around the shaft, another option would be to make your shaft and take it and the base plate over to the machine shop and have em put brass bushings in the base plate and hone the bushings for the proper fit to the shaft.....