I do develop single source cross-platform apps for Win, Linux, MAC, Android and iOS. After you get the basics per platform, it's simple to port them :)
Your pro file requires to have containers for platform specific code like JNI on android or the icons on iOS.
E.g:
@android {
QT += androidextras@
or
@ios {
BUNDLE_DATA.files = $$PWD/iosImages/Icon-60.png @
I'm unsure about Qt 5.3, but with 5.2 I had problems using SSL connections on iOS. Such problems you need to add exceptions for the platforms with QtGlobal.
@#ifdef Q_OS_ANDROID
#endif@
Would only compile the code between if the target is an Android device.
You do not need any special Qt version, the basic free one is fine.
Libs are added as always, using your .pro file and
@LIBS +=@