I took me quite a while to find out how to do this in QT5 without qml and too much work. So thought I'd share:
#include <QCoreApplication>
#include <QGuiApplication>
#include <QKeyEvent>
void MainWindow::on_pushButton_clicked()
{
Qt::Key key = Qt::Key_1;;
QKeyEvent pressEvent = QKeyEvent(QEvent::KeyPress, key, Qt::NoModifier, QKeySequence(key).toString());
QKeyEvent releaseEvent = QKeyEvent(QEvent::KeyRelease, key, Qt::NoModifier);
QCoreApplication::sendEvent(QGuiApplication::focusObject(), &pressEvent);
QCoreApplication::sendEvent(QGuiApplication::focusObject(), &releaseEvent);
}
The clue here is that by clicking buttons (if you would manually make your keyboard), launches a sendevent to the current object thas has focus (for example a textbox). You could of course hardcode a textbox, but that only works if you have only a single input to use your keyboard for.
The last thing you have to make sure, is to set the focusPolicy of your keyboard buttons to NoFocus, to prevent focus from shifting when the keyboard is pressed.
Credits go to https://www.wisol.ch/w/articles/2015-07-26-virtual-keyboard-qt/
Hope this helps someone.