there are 2 functions that are currently not documented, but which you can use to pause and resume your game manually. You can have a look in the Squaby demo or wizard in the SquabyScene.qml and search for system.resumeGameForObject() and system.pauseGameForObject().
What these functions do, they pause and resume all Timers and animations for the children objects of the item you provide them as a parameter. You can try to click the menu button in a Squaby game, and you will see the level creation and entity movement is paused. So you could trigger a call of pauseGameForObject() when the onApplicationPaused() signal handler is called in GameWindow, and resumeGameForObject() NOT in resume, but when you press your resume button in the game.