https://gist.github.com/Tosainu/c451e277912cc7e605f7 のゴリ押し解決案

main.cc

#include <QCoreApplication>
#include <QJsonDocument>
#include <QJsonObject>
#include <QJsonValue>
#include <QString>
#include <QDebug>

class JsonValue : public QJsonValue {
public:
  JsonValue(QJsonValue&& value) : QJsonValue(value) {}

  JsonValue operator [] (const QString& key) const {
    return toObject().value(key);
  }
};

class JsonObject : public QJsonObject {
public:
  JsonObject(const QJsonObject&& o) : QJsonObject(o) {}

  JsonValue operator [] (const QString& key) const {
    return static_cast<JsonValue>(this->value(key));
  }
};

int main(int argc, char *argv[]) {
  QCoreApplication a(argc, argv);

  JsonObject json = QJsonDocument::fromJson(QByteArray(R"(
    {
      "relationship": {
        "target": {
          "id_str": "12148",
          "id": 12148,
          "screen_name": "ernie",
          "following": false,
          "followed_by": false
        },
        "source": {
          "can_dm": false,
          "blocking": null,
          "muting": null,
          "id_str": "8649302",
          "all_replies": null,
          "want_retweets": null,
          "id": 8649302,
          "marked_spam": null,
          "screen_name": "bert",
          "following": false,
          "followed_by": false,
          "notifications_enabled": null
        }
      }
    }
  )")).object();

  qDebug() << json["relationship"]["source"]["screen_name"].toString();

  return a.exec();
}