Hello fellows.
Here instructions for building Qt 4.7.
You can use part of or all of Qt for Haiku. Qt should all work. You said your application only needs QtWebKit. This will depend on other libraries so you have to include them too or tell users how to get them.
The problem with dependencies is one library may have a couple and then you have to check those dependent libraries too and they may have the same or different dependencies. You only have to include libraries not already in Haiku. To only provide required libraries, you would check dependency of your program and then dependencies for those linked in libraries.
QtWebKit comes with Qt. You might be able to swap newer Qt WebKit but it could introduce bugs, or not work well and not sure what changes were done to Qt WebKit for Haiku. Lots of headaches and not worth the effort. I would suggest not trying to change it out. Better to switch to Qt4.7 for newer Qt WebKit when finished port becomes available.
Thanks RISC. Thread is too long for me to remember.
I just took the link 3deyes recently gave here and posted it:
http://haikuware.com/general-software/1329-qt4-applications#1337
Great news, did not realize that 4.7 was almost ready for release!
Building Qt 4.7 instructions
http://qt-haiku.ru/index.php?option=com_content&view=article&id=53&Itemid=67
Seems like they got some applications working. So, I would guess Qt 4.7 is in an early working state. Not sure how far along they are with the port.
Actually I gave link above about building instructions.
BTW, 3deyes says that soon they will make Qt4.7 package.
Thanks for the info, i will just build 4.7 on haiku i think, i have enough bugs in the applications as it is without introducing bugs into the framework lol thanks for the help, no doubt ill be back to you with this one!
Ok well its been compiling for 5 hours now! i will tell you if i have it and the application running by tomorrow 
Ok good news, got the whole thing compile and my application compiles perfectly! Better still its fully operational, thanks for the help guys
Qt 4.7 first preview build:
http://qt-haiku.ru/index.php?option=com_rokdownloads&view=folder&Itemid=60
qutIM rebuilded with qt 4.7 - http://qt-haiku.ru/index.php?option=com_rokdownloads&view=file&Itemid=61&id=71:qutim-0-2-qt4
vacuum-im (jabber client) - http://qt-haiku.ru/index.php?option=com_rokdownloads&view=file&Itemid=61&id=70:vacuum-1-0-2-qt4
Arora browser - http://qt-haiku.ru/index.php?option=com_rokdownloads&view=file&Itemid=61&id=74:arora-0-10-2-qt4
Most programs compiled for Qt 4.5 will work in 4.7 without recompilation. For example all the games from our site.
there is a minor bug that i found.
If you open an qt programm and you go to the menu-bar and open a menu, then you can click on the title-bar of the window (also the frame of the window) and you can start to move the window around, but the menu that was opened, keeps being opened (displayed) at the same place. Perhaps it should disappear once the user clicked on the title-bar/frame.
Arora works now really great with qt 4.7