You are not the first one with this issue:
https://github.com/dryoo/dokuwiki-plugin-shortcutkey/issues/6
If one uses URL-Rewriting to eliminate the need of "doku.php" in the URL, the plugin works like expected.
The demo page for the plugin (
http://openwiki.kr/tech/shortcutkey) uses URL rewriting.
Well, i could add it statically, but i don't think it is a good idea because there may be setups where this is hidden or something different. Or is it usual to concat ["DOKU_URL"] with "doku.php" ?
I think by the above given link to the specification of DOKU_URL your question should have answered.