This patch isn't going to work properly as the do_export takes two arguments, but using a keyboard shortcut in the given manner is only going to do what you are expecting it to.

What is the expected behavior when the user uses the keyboard shortcut Control-E? Is this just going to display the export menu (same as clicking the export button in the header) and given the dropdown menu focus? Or are you expecting the last selected export type/options to be applied on the current image? The desired effect will need to be coded as such.

Additionally, keyboard shortcuts are recorded in the data/com.github.phase1geo.annotator.shortcuts.ui file so that the user can see them when using the keyboard shortcut cheatsheet. I also like to add the keyboard shortcut within a tooltip using the Utils.tooltip_with_accel() function -- one should be added to the export header button tooltip.

If you are willing to add these changes, I can approve the pull request.