It is not crystal clear for new users, what the difference between the login and sign-on is. In addition, it is confusing that if the sign-on field contains anything, like a white space, character, the user cannot edit the login fields. There is a good logic behind, but it's not clear to the user.
It would be better to separate the sign-on page completely from the the login page. The login page contains the login fields and a button to navigate to another page, if the user does not have a Qt Account.
Look at the attached wireframe for reference.