As you have guessed, we no longer officially support Qtopia. The last released version was named Qt Extended 4.4.
While you may not have found any info specifically related to your board, this is not that strange because Qt doesn't contain anything specific to a particular hardware board. Qt supports the ARM architecture you are using as well as your kernel version so that is most likely enough. Assuming that you have a working cross-compiler installed on your host PC, then the next step is to download and cross-compile Qt Embedded using the device's toolchain. I recommend starting here:
Getting things like the touchscreen working may require some tinkering, but you might be able to find some code for this in the Qtopia package released by the manufacturer. It could be as simple as porting their Qt 2 based code to Qt 4.