Are you really just wanting the icon to the file of the document? Since this is what is displayed in the title bar of a document's window, you can use NSWorkspace's iconForFile: method and set the returned image's size to 16x16 using setSize:
Type command-space, then "proxyicon". On my machine, it finds among other things "Window Manager Reference", which will tell you how to add a proxy icon to a window, how to get the icon, how to handle dragging it etc. in Carbon applications.
Thanks. The Window Manager looks like the real deal. However, I have no experience programming in Carbon and therefore have no idea how to get a reference to the aforementioned Window Manager. I would appreciate any guidance.