There were C# Qt bindings since many years ago but those were not official supported so the quality was not that good,once there was a Java official binding/port that was dropped after a short time, I would not use someone's hobby bindings for a real world project(I mean a project with many users that you need to support for years , through OS and oteher system updates)
Sounds like a nice project, I did not want to insinuate that the quality is not good, I did not used Qt in a few years(since Qt4 days) so I am not sure about QML, without doing any research I think I am inclined to use the classic QtWidgedts for a desktop applications, SQML seems to me more mobile or designer first toolkit.
I strongly believe that Microsoft made a huge mistake not making .Net WPF and Silverlight cross platform and open source it. they would have made money by selling the Visual Studio IDE,