Thank you wysota for your reply!
If I started with this project I read a lot about MVC and the Qt models. I thought that it would be very complex to implement my own model based on QAbtractItemModel.
And I wasn't sure if this will be really necessary. So for the first step I decided to use QStandardItemModel and expand it with my needed functionality. And everything works fine except the above written performance problem.
Do you think I can fix the problem by deriving from QAbstractItemModel?
Is there a good tutorial on how to do this? (I've found a link to a tutorial on this forum but I get an 404 Error...: http://doc.qt.io/qt-5/itemviews-simpletreemodel.html)
On which point do I have to ensure that I will not run to same trouble as I get with QStandardItemModel?
Is it only a problem of the model or also the view?
Is there no other QStandardItemModel based solution?

Thank you for your help!!