In Ubuntu 12.04 the libgdal version is 1.7.x and QLandkarte 1.4 needs libgdal1 => 1.9.1.
To enable packages not in the standard repos you are going to need to use PPAs
These 2 appear to fit the bill.
Please note the description of the second -
In fact - with any PPA you need to be aware that it is not official, this answer has more detail - http://askubuntu.com/a/35636/2018
To install from a terminal
Then run these one at a time - follow the instructions
You should then be able to install (or update) qlandkarte
You can also add them into software sources from a GUI