This is a list of some Qt and not only, IDEs that will shorten your development time with Qt. Some of them are plugins and some others are standalone development enviroments.
As described in Wikipedia:
Qt is a cross-platform application development framework, widely used for the development of GUI programs, and also used for developing non-GUI programs such as console tools and servers. Qt is most notably used in KDE, Google Earth, Skype, Qt Extended, Adobe Photoshop Album, VirtualBox and OPIE. It is produced by Nokia's Qt Development Frameworks division, which came into being after Nokia's acquisition of the Norwegian company Trolltech, the original producer of Qt, on June 17, 2008. Qt uses standard C++, but makes extensive use of the C pre-processor to enrich the language. Qt can also be used in several other programming languages via language bindings. It runs on all major platforms, and has extensive internationalization support. Non-GUI features include SQL database access, XML parsing, thread management, network support and a unified cross-platform API for file handling. Distributed under the terms of the GNU Lesser General Public License (among others), Qt is free and open source software.