It's a Georgian style cabinet, probably mahogany. Since it has been "up scaled" and painted and distressed and the glass replaced with wire, I m not sure why it matters if it's missing a piece of molding since the corners and edges have been sanded and scuffed up and the brasses replaced with work shop hardware. But a half round dowel of the proper size will do.

It appears to be half-round. If the profile is something else, pull the pins on the door hinges (or remove the hinge halves) and take the door to a wood shop. Various profiles can be duplicated with dado cutters.