How to make rods for fabric insert shutters

My house was built in 1960 and one BDR has the original fabric insert shutters. Some of the rods are broken and I want to make new. Seems like it should be pretty simple, but having no luck finding someone with the tool/knowhow. I assume a lathe is needed. A router also? If so, which bit. Starting with an 11-1/4” length of 3/8” dowel rod, one end needs to be cut down to 1/2” and the other end 1/4” with both ends having a diameter of 1/4”. Cannot use 1/4” for the entire length because it isn’t strong enough.

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Harvard Study: Home remodeling gains to remain robust

CAMBRIDGE, MA – Strong growth in home improvement and maintenance expenditures is expected to continue over the coming year, according to the Leading Indicator of Remodeling Activity (LIRA) compiled by the Remodeling Futures Program at the Joint Center for Housing Studies of Harvard University.  The LIRA projects year-over-year gains in annual improvement and repair spending will reach 9 percent in the fourth quarter and maintain that pace into 2022.