Nokia bought the Qt (pronounced “cute”) team before they made the deal with Microsoft to run WP7 on their smartphones. Back then, the old CEO was still hoping Symbian will survive the iPhone and the onslaught of Android phones coming into the market. But Symbian used to be very painful to write apps for, and they needed better tools to get developers on board. That's how they ended up with Qt, which had some of the best development tools in the industry.
But then that whole plan crashed and burned as the new CEO, Stephen Elop, made the deal with Microsoft to basically outsource all OS development to them. This meant that Qt was no longer necessary, because it couldn't be used for WP7 apps, nor would Microsoft want it to be used like that, as they would prefer developers to use their own Visual Studio.
A lot of developers have been concerned about the future of Qt now that Nokia does not have a use for it anymore. Fortunately, they've decided to sell it to Digia, which has committed to take good care of Qt and further develop it. Digia goes as far as to promise that they will include support for Android, iOS, and even Windows 8 in the future.
Android doesn't exactly have the best tools for development. Even Eclipse, the most popular IDE for the platform, is often called clunky by developers. Android could probably find good use for some quality alternative development tools like Qt. The problem is that apps would have to be either written in native C++, or they will need to be somehow converted into Dalvik apps. That depends on what path Digia wants to take for Android development. However, I figure the conversion route would be a lot more popular if they can make it happen. Such a project would involve a lot of work, though.
Another thing Digia could do is try to help developers make cross-platforms apps between Android, iOS and Windows 8. That could be truly game-changing. But again, it would be an incredible task. Digia is probably more focused on helping the Qt team finish the Qt version 5.0 right now, so it can launch next month, as scheduled. But we'll see what the future brings us with QT 6.0 and what kind of Android support it will receive.