The version 4.4 of QT might not be available on old distributions. Ubuntu provides QT 4.4 backports for Hardy but not for Gutsy. Debian testing and unstable contain QT 4.4 but not the Debian stable. If your distribution does not provide QT 4.4, you will have to compile it yourself. This is easily done on Debian and Ubuntu with the following: 

# You will need these packages
sudo apt-get install wget fakeroot dpkg-dev
mkdir qt
cd qt
wget http://ml.nec-labs.com/download/qt/qt4-x11_4.4.0-4.dsc
wget http://ml.nec-labs.com/download/qt/qt4-x11_4.4.0.orig.tar.gz
wget http://ml.nec-labs.com/download/qt/qt4-x11_4.4.0-4.diff.gz
dpkg-source -x qt4-x11_4.4.0-4.dsc
cd qt4-x11-4.4.0
dpkg-buildpackage -rfakeroot
The command dpkg-buildpackage might complain for some unmet dependencies. Install them with apt-get install, and then execute the command again. The compilation takes around two hours on a recent computer. You can then install all the packages it created with: 
cd ..
sudo dpkg -i *.deb
For distributions not Debian-based, please refer to the documentation for compiling packages. You might also be able to find QT 4.4 binary packages on the web.

We provide ourselves binary packages for some architecture.