You can't have two different versions installed from packages at the same time. Removing 3.x is a very bad idea, so the way to go is to install 1.44 from source. Note that it's not an easy task. Qt requires quite many libraries and it may be (or, rather, it is) that 1.44 requires much older versions than the ones you have. It'll require you to install old versions of the libraries also from source, not packages.
I assume you know how to deal with gcc and that you have make, automake and similar tools from Development section. You probably also have Qt 1.44 source. If not, download from Trolltech site. Now, choose a directory you want to buld it to. It may be in your home dir. Unpack Qt 1.44 to the choosen location.
I don't remember Qt 1.44 copiling options, but in the older versions you had to set QTDIR. Set it. Example: when you have it unpackaged to /home/yourname/qt, QTDIR should be set this way:
Code:
export QTDIR=/home/yourname/qt
Now try to compile it. First run ./configure, then make. You may get into dependencies problems during the process. Read error messages carefully. If you get one about missing libraries, note down the required version, download it and compile like the instruction says (usually ./configure, make, make install).
Note: You may choose to remove Qt 3 and install 1.44 instead. It'll cause KDE and many other apps to be removed as well, however.