If you want to take contributions, look at the details of codeplex.com to see if that would suit you. I haven't tried it (putting code on the site), but apparently you can use not only Git, but also TFS (which is easier to deal with in my opinion). Visual Studio comes with TFS support built in, and it may or may not play nicely with Qt.
Or you could look for alternatives. Perhaps give write access to some that are interested in Drop Box and manually log changes.