Adding Qt libraries to existing game engine

[Illogica]

Hello,
I would like some advice on how I should proceed.
I'm trying to add Qt bindings to the Tesseract engine . The engine is basically mostly graphics, I want to try and expand the server side using Qt.
I successfully ported the Makefile to qmake, (and it was quite an endeavor by itself...).
Now I need to exchange data between Tesseract and Qt, so I'm trying to #include Qt in the Tesseract source files, but Tesseract uses a lot of globals and I get a crazy amount of errors like this:

In file included from ../tesseract-nightly2/src/qt/bridge.h:16:0,
                 from ../tesseract-nightly2/src/qt/hooks.h:5,
                 from ../tesseract-nightly2/src/qt/hooks.cpp:1:
../tesseract-nightly2/src/shared/tools.h: In function 'void* operator new(size_t, void*)':
../tesseract-nightly2/src/shared/tools.h:36:14: error: redefinition of 'void* operator new(size_t, void*)'
 inline void *operator new(size_t, void *p) { return p; }
              ^
In file included from E:/Qt/Tools/mingw492_32/i686-w64-mingw32/include/c++/bits/stl_construct.h:59:0,
                 from E:/Qt/Tools/mingw492_32/i686-w64-mingw32/include/c++/bits/stl_tempbuf.h:60,
                 from E:/Qt/Tools/mingw492_32/i686-w64-mingw32/include/c++/bits/stl_algo.h:62,
                 from E:/Qt/Tools/mingw492_32/i686-w64-mingw32/include/c++/algorithm:62,
                 from ../../../Qt/5.6/mingw49_32/include/QtCore/qglobal.h:85,
                 from ../../../Qt/5.6/mingw49_32/include/QtCore/qcoreapplication.h:37,
                 from ../../../Qt/5.6/mingw49_32/include/QtCore/QCoreApplication:1,
                 from ../tesseract-nightly2/src/qt/hooks.h:4,
                 from ../tesseract-nightly2/src/qt/hooks.cpp:1:
E:/Qt/Tools/mingw492_32/i686-w64-mingw32/include/c++/new:146:14: note: 'void* operator new(std::size_t, void*)' previously defined here
 inline void* operator new(std::size_t, void* __p) _GLIBCXX_USE_NOEXCEPT
              ^
In file included from ../tesseract-nightly2/src/qt/bridge.h:16:0,
                 from ../tesseract-nightly2/src/qt/hooks.h:5,
                 from ../tesseract-nightly2/src/qt/hooks.cpp:1:
../tesseract-nightly2/src/shared/tools.h: In function 'void* operator new [](size_t, void*)':
../tesseract-nightly2/src/shared/tools.h:37:14: error: redefinition of 'void* operator new [](size_t, void*)'
 inline void *operator new[](size_t, void *p) { return p; }
              ^
In file included from E:/Qt/Tools/mingw492_32/i686-w64-mingw32/include/c++/bits/stl_construct.h:59:0,
                 from E:/Qt/Tools/mingw492_32/i686-w64-mingw32/include/c++/bits/stl_tempbuf.h:60,
                 from E:/Qt/Tools/mingw492_32/i686-w64-mingw32/include/c++/bits/stl_algo.h:62,
                 from E:/Qt/Tools/mingw492_32/i686-w64-mingw32/include/c++/algorithm:62,
                 from ../../../Qt/5.6/mingw49_32/include/QtCore/qglobal.h:85,
                 from ../../../Qt/5.6/mingw49_32/include/QtCore/qcoreapplication.h:37,
                 from ../../../Qt/5.6/mingw49_32/include/QtCore/QCoreApplication:1,
                 from ../tesseract-nightly2/src/qt/hooks.h:4,
                 from ../tesseract-nightly2/src/qt/hooks.cpp:1:
E:/Qt/Tools/mingw492_32/i686-w64-mingw32/include/c++/new:148:14: note: 'void* operator new [](std::size_t, void*)' previously defined here
 inline void* operator new[](std::size_t, void* __p) _GLIBCXX_USE_NOEXCEPT
[...]

How would you suggest I go on? Is there some way I could try to avoid these collisions between Tesseract sources and Qt? Can you eventually point me to some work somewhat similar to what I'm trying to achieve?