It would be much easier if you can find a replacement of the third-party MFC library.
The third party library, static or dynamically linked, would require an MFC version that is exactly the same version as the one used to compile the third party lib file. MFC classes are not binary-compatible between versions and not even binary-compatible between configurations (static/dynamically linked MFC & CRT, single/multiple threaded CRT, debug, release, X86, X64, MBCS, UNICODE, etc) of the same version.
If you use CString::LoadString or anything else that access the MFC module state it would require a global CWinApp. An easy way to get it is to create a regular DLL. Adding one to your QT project would require you to move code from your exiting entry function to InitInstance and ExitInstance.