I have gotten several somewhat complex programs based on the SDL 1.2 library to work on Android. The code base for that is here -
Pelya's port of SDL 1.2 to Android has support for joystick controls (which it can mimic on-screen, and which you can extend). I have done experimental ports that use the joystick, although none of my releases yet have utilized that feature.
As far as qt, the qt lighthouse project for Android is codenamed necessitas, and is located here http://sourceforge.net/p/necessitas/home/necessitas . I don't know firsthand how far along their port is, but their project is your best bet.