@Kraken
No. I did it that way:
1.) Compile against the system's Qt version on the target machine. (ie. install Qt through apt-get system-wide, then use the system Qt to compile).
2.) You can use debreate to guide you through the whole process of creating a deb package. At some point you will have to enter your apps dependencies. To find out what these are, you can use dpkg. (don't exactly remember the commands, dpkg -S and dpkg -s, you need to do some research here. Those will show you the exact version your binary depends on). When you distribute your app via deb, the correct dependencies will be installed on the target machine then.