You can use not predefined days name

QLocale locale = QLocale::c();
for (int i = 1; i < 8; ++i) {
    if (weekday.startsWith(locale.dayName(i, QLocale::ShortFormat), Qt::CaseInsensitive)) {

"i" and "l" local variables are hard to read, please rename to locale or cLocale

You could (and probably should) do like the above loop and move QLocale::c() to a local variable defined before the for loop.
QLocale::c() creates a QLocale instance every time, so better do that only once.