Rather than x/qt on OZ, you can try to use OZ/gpe as this flavor uses X rather than qt/embedded+opie.
OZ uses http://www.openembedded.org/
for cross compilation
They may have a prebuilt sdk, onboard compilers are also available.
I let the oz developers give you more and more accurate information about this.
Pdaxrom releases a cross sdk and a native (onboard sdk) you can find them here : http://220.127.116.11/rc11/Zaurus-7x0-860/
They are both simple to install and to use.
Another possibility you did not mention is x/qt on a sharp based distribution.
I don't believe that qt4 has been compiled for any platform yet so you'll have to do it.
Finally instead of building your application without modifications, you might want to modify your code and port your application in order to make it work with qt3 or qt(2?) /qtembedded or opie libraries and mysql versions that are available now.