Is there a safe way to rip a 1-inch dowel on a table saw?

I would not feed a round dowel directly against the fence. It can roll or twist into the blade, and a long piece that is not perfectly straight can bind. A push stick does not solve those problems.

If half-round trim will do, buying it is the simplest option. Otherwise, a bandsaw with a properly secured V-shaped holding jig is a better fit for round stock, though it still needs careful setup and safe handling.

There are table-saw jigs made to capture cylindrical stock, but that is a different proposition from holding a dowel by hand. The jig would need to prevent rotation and keep the work firmly controlled throughout the cut. If you do not already have a well-designed fixture and know how to use it safely, I would choose another method.

Also check the dowel for bow or internal movement. Either can make a long rip less predictable.

For a one-off, I would skip the saw and make the shape from flat stock instead, or use a hand plane to form a half-round. It takes longer, but avoids trying to steady a round piece beside a spinning blade. A trim supplier may also carry the profile you need.