I am a bit confused what you are asking as you use the term round over and then bevel
are you beveling so it's 8 sides? or rounding over so it's a dowel?
the problem with rounding over a 1" square is the bearing ends up riding on a part of the curve and gives you less than a dowel in the end.
Your best bet is to chamfer(bevel) the corners off. That can be done at least 3 ways, table saw, band saw or a router with a chamfering bit.
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