SIGSEGV in QFontDatabase when attempting to use QTextDocument::drawContents in a QCoreApplication

QTextDocument::drawContents needs a QGuiApplication to work, because it uses QFontDatabase. The documentation of all the classes involved in the example below fails to mention this (AFAICS). I would expect the unapplicable method (in this case QTextDocument::drawContents, perhaps there are others?) to return an error, but instead it makes the application crash with a segfault in QFontDatabase::findFont(QFontDef& const, int).

#include <QCoreApplication>
#include <QTextDocument>
#include <QPainter>
#include <QImage>
#include <QRect>

int main(int argc, char *argv[])
{
    QCoreApplication a(argc, argv);
    QTextDocument d;
    QImage image(128, 128, QImage::Format_ARGB32);
    QPainter p(&image);
    d.drawContents(&p, QRect(0, 0, 128, 128));
    return a.exec();
}