Qt is great for making GUI, so keep it close for your game editor, especially if C#/.NET is not an option.
For a game though, I would avoid it personally. For all its advantages, Qt is bloated and what was once a GUI library is now an entire framework with a breadth that rivals that of the .NET or Java library. Might sound useful to have a wide library for a game, but in reality a lot of the non-GUI related utilities are already provided (and usually in a much better way!) by boost and/or the C++ standard library anyway, so you don't really need it if you're not going to use Qt for heavy GUI building.
Now, you absolutely can use Qt for a game, and it's going to work, but you're looking to include a massive DLL that you'll barely use. I think it'd be better advised to use something like SDL to get a base game windows and collect basic events if you absolutely want cross-platform ability; that's exactly what it's made for, and for having used it extensively in the first versions of my RPG I can say that it works really smoothly.