How simple would this be to port a Qt 4 native app to a Qt mobile app? Does it change the library or add touch events? Are there system specific calls that have to be made like Windows and iOS have?
What do you mean? Qt apps work on mobile without any changes in code... (but usually, it's a good idea to have a different UI for mobile apps - because screen sizes are different, and of course the input differs, too).
Also, you have to keep in mind that if you use Qt on certain mobiles, you don't have Qt GUI library support, and instead you'll have to build all your UI with something like QML.