You could export a page, then import it to a destination page, which would include the widget configuration. It does mean it copies ALL the widgets, and doesn't target a single widget.
It'd be really nice if there were some script APIs that allowed for;
Copying the page layout from one place to another. I've developed my own helper API for this, but having it in the core platform would be a big plus! Mine will essentially do an export of the page layout into a string (XML), then you can tinker with the XML before you write it over the top of a target page.
Copying widget configuration from one widget to another
Programmatically add/remove/edit/move a widget on a page
