Hi. I think most of your requirements rely more on the operating system than on Qt. The only problem I see is the virtual keyboard. The one Qt has is available only under a commercial license. If you don't have one, you would have to make your own. It's boring, but it can be done.
Of course it will not be easy at first, as you have no previous with Qt or C++, but once you learn it, you'll have a major advantage for future projects.