Don't try to prevent inlining unless you really know what you are doing. The library isn't designed to intentionally inline code that doesn't make sense to inline.
For Qt's math and similar functions, you'll almost certainly be fine on the performance front. If you ever find out you're not, it's not all that hard to replace the functionality you were using anyways.
For Qt's more generic tools, where performance will eventually kill you is state changes. If you're going to have simple scenes in your game, Qt will probably work well enough. If you're going to have complex scenes, Qt will be causing more state changes than you want behind the scenes.
Is there a reason you don't want to use an actual game engine or libraries specifically designed for games? When something is designed for games, it's going to optimize for animations, character movements, culling excess polygons, etc. When something is designed for general purpose use, it's going to optimize for a UI that probably only has a small portion changing, and probably with very simple changes at that.
Edit: BitMaster's point about just plain missing features essential for game development is probably even more important than performance. I haven't given much thought to this idea of using non-game tools for games, so there are probably other things I'm missing as well. Unless you can outweigh the concerns with significant benefits, I'd recommend just using actual game development tools for developing games.
Edited by richardurich, 20 January 2014 - 07:44 AM.