I need to fill in the handle holes on a dresser and redrill them.
either wood filler or glue and dowel


That's what I would do. I would choose a wood filler that says on the tin that it can be redrilled. You might be able to use a repair-washer on the back to spread the load if you are worried.

Otherwise I'd drill the hole out to the next largest dowel size, glue in a dowel and use a flush-cut saw.

If necessary, you can improvise a dowel by drilling a hole in any convenient bit of steel and using that as a "dowel plate" through which to hammer some slightly oversized wood rod. Chucking the wood in a hand-held drill can work to speed up the production of the dowel.