Here's a couple of ideas.
A dowel plate. A piece of steel with a 1 inch hole is one way. See the
Lie-Nielsen dowel plate as an example.
I saw an episode of the woodright shop in which Roy Underhill used a dowel
plate to make dowels for a wooden rake. It is simplicity in action, however
like all non-electric woodworking it isn't necessarily easy work.
The Lie-Nielsen website includes a PDF from David Charlesworth explaining
dowel plates and another method using a section of pipe.
Either of those hand tools would be more to my liking than trying to use a
router table and roundover bit.
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