Follow the link to download the QtSDK. That provides all you need for Qt development. Also it's distro agnostic so the latest QtSDK installer will be ok for Ubuntu 12.04. It includes QtCreator, an 'official' IDE for Qt development, Qt for desktop and mobile targets (Symbian and Meego), QtDesigner - historically a tool for creating GUIs but since Qt Creator was released it's now integrated in Qt Creator, Qt linguist - a tool for your applications internationalization, and Qt Assistant - all in one tutorial, help, and examples application.
With QtSDK itself you'll be able to compile apps for your Desktop Linux. To be able to compile apps for your target board I guess you have to install the tool chain for it that includes a Qt version for the selected target, cross-compiler/libs, etc. If you target other Desktop OSes as well, you'll need the related tool chain as well.