A few months ago when I was experimenting with Qt's Widgets, I ran into this issue too.
My ultimate suggestion would be to use QML instead of QWidgets, since they're tailored for touchscreen interfaces. Moreover, it will ease your progression to Cascades.
That being said, if you want to resolve your issues now, I can make some suggestions. Basically, Qt is defaulting to a certain UI style, where the sizes are "small". It's expecting that you're using a mouse and keyboard, so it's sizing controls according to that.
The solution is to make the controls bigger. While each widget does have its own methods to do that, the beauty of Qt is the ability to apply stylesheets for your entire application. It's great, since you can have a consistent look and feel across your applications.
For your scenario, you could use the stylesheet to adjust the default sizes for the controls you're using.
http://qt-project.org/doc/qt-4.8/stylesheet.html
That link should get you started with everything you should need to accomplish what you're looking for.
Good luck!
