I buy and use 1/8" birch dowels for a lot of things, mostly as actual dowels; hidden pins to align things. For plugging holes in a visible surface, I prefer to cut my own cross-grain plugs from matching wood.
Plug cutters are real easy to make from a piece of tubing, hand filing some teeth on the end of it. I have a machine shop here, so I make up core drills, which are a nicer version of the same idea:
I made these for cutting dots from synthetic pearl stock, but they work fine for wood too. These are turned in a metal lathe, from round steel or stainless bar stock. The ID is bored to exactly the diameter of the dot I need. The OD at the end is turned down to make the cutter thin wall. The inside of the shank is drilled hollow, a little larger than the dot diameter. That way, the dots will stack up neatly inside the bit, and can be easily dumped out the back end. The teeth are hand cut with a file.
You can make up plug cutters similar to this from steel tubing, filing the teeth by hand.
For larger diameter plugs, I use a router lathe setup. I mounted a RotoZip electric cutter head to the tool post of an older backup metal lathe. With this, I can make plugs and dowels to precise diameters, any wood, any grain orientation. I run the lathe spindle fairly slow, like 180 rpm. Most of the cutting is done by the router bit at speed in the RotoZip head. It leaves a very smooth surface.
You can make a setup like this, mounting a small router head, or even a Dremel, onto a small cheap wood lathe. Turn the spindle slowly by hand and bring the spinning cutter against it.