there is the jet mini which is very good (i have one). However, given what you want to achieve with it, the cheapest of lathes should be suitable. it isn't like you are starting with a tree and wanting to produce big items.
turning such small stuff sounds easier than it is though. i think that i would remove the corners of a square blank the best that i could, and then put it in a cordless drill. using sandpaper i would bring it to properly round.
or look at the veritas dowel makers. various styles available, here is one
http://www.britishhardwoods.co.uk/verit ... utter.html