While the question assumed that Xephyr was run correctly (since no information is provided on this), I have at least confirmed that qBittorrent runs fine in Xephyr on Debian Xfce Wheezy.
The screenshot below is showing qBittorrent 2.9.8 in Xephyr.

This was tested on Debian Xfce Wheezy and using latest packages of libqtcore4 and xserver-xephyr available to this date, which are similar to versions quoted in the question.
$ lsb_release -a
No LSB modules are available.
Distributor ID: Debian
Description: Debian GNU/Linux 7.9 (wheezy)
Release: 7.9
Codename: wheezy
$ dpkg-query -W | grep libqt
libqt4-dbus:i386 4:4.8.2+dfsg-11
libqt4-network:i386 4:4.8.2+dfsg-11
libqt4-xml:i386 4:4.8.2+dfsg-11
libqtcore4:i386 4:4.8.2+dfsg-11
libqtdbus4:i386 4:4.8.2+dfsg-11
libqtgui4:i386 4:4.8.2+dfsg-11
$ dpkg-query -W | grep xephyr
xserver-xephyr 2:1.12.4-6+deb7u6
Identifying the issue
The only relevant search I found was Bug 71421, reporting on "Qt5 apps don't work with Xephyr".
When trying to run any Qt5 (or apparently GTK3) apps inside Xephyr, they don't work (as in nothing is shown). GTK2 or Qt4 works just fine as well as GLX apps (glxgears for example). Also tested on standalone X server with no DM running - Qt5 works perfectly fine there, just inside Xephyr they don't.
This bug is similar to the question case, except affecting only Qt5 applications. The bug was due to Qt5 and it was fixed recently in late April this year.
Besides that, there was no information provided on how the application was run in Xephyr.
The above applications work when started in normal X server, but when I start them in Xephyr, I only see the window frame, but it is blank.
Based on the quoted text, I have something else to doubt: Did Xephyr run with invalid arguments? Or rather, how was the application run as another user in Xephyr?
If you are indeed sure that Qt4 applications don't work in Xephyr, it may be an unreported issue in Qt4 package. But since I have confirmed that qBittorrent (based on Qt4) runs fine in Xephyr, it may be an issue with the "another user" or the way Xephyr was run from current session.
On Xephyr usage
These are some online sources that explain about using Xephyr to accomplish certain tasks.
Xephyr on ArchWiki. A good place to get started for running Xephyr, but doesn't explain much on extensive usage besides running a Terminal or Window Manager in Xephyr.
No idea how to get started with Xephyr. What am I doing wrong? on Xorg mailing list, dated Thu Jan 23 17:16:40 PST 2014. Another way of running Xterm in Xephyr.
How to run multiple X desktops? on Super User, asked Jul 22 '09. One of the answers suggested to use Xephyr. Similar way as suggested in source #1.
Multiseat Configuration/Xephyr: How to make a Multiterminal with Xephyr on Wikibooks.
Screenshots from multiple Xservers on Unix & Linux Stack Exchange, asked Aug 21 '14.
Howto: run firefox (and other things) as a separate user with Xephyr. This seems to be the most similar usage as hinted in the question.
The reason I have quoted these sources, is to provide relevant hints that may help you to clarify whether you are running Qt application in Xephyr correctly or else.
That being said, there is something tricky for understanding the first sentence "using Xephyr to run applications as another user, while logged in as primary user". After all, I didn't create "another user" for test running qBittorrent in Xephyr. Perhaps someone else can give a better answer.