You are much better off with setting up global shortcuts for mpc, with xbindkeys. This lets you to control your mpd not depending on any running clients.
However, global shortcuts of QMPDClient functions may be useful as well and may be implemented some day. Especially if someone makes a patch.
As you can see, I can't reproduce this problem.
The real problem is, your window manager does not resize QMPDClient to required height. File a bug against it instead.
Uh, I can't take credit for that. QMPDClient is originally developed by Håvard Tautra Knutsen, I've just picked up its development when Håvard stopped it. But thanks anyway :)