As I indicated in my comment, you have to fix this first issue:
instead of:
QVariant variant;
variant.toString() = "AA";
you should write
QVariant variant = QLatin1String("AA");
In general, you would look into the setData(...) implementation for such cases whether you emit the data changed signal properly and so forth, but here you are entering a prior issue which can lead to problems, so let us fix that.
Note, you should use QLatin1String to avoid the unnecessary explicit conversion from raw char* to QString. This is a good practice in general, and this is available with Qt 4 as well as Qt 5.
Although, you could also use the QStringLiteral macro for creating a QString very efficiently with template magic out of your raw literal, but that requires C++11.