printFormatModel.data(printFormatModel.index(1,1),"idRole")

Second parametr in this case for method data would be "idRole" which is string, while model waits for some integer value. When you use it like

printFormatModel.data(printFormatModel.index(1,1),1)

Your second parameter would be 1. But according to your code modelIndex at PrintFormatModel::data would be invalid, since Qt::UserRole is equal to 256, you will get 1 - 256 - 1 for columnId.

printFormatModel.data(printFormatModel.index(1,1),"idRole")

It's my model:

#include "printformatmodel.h"

PrintFormatModel::PrintFormatModel(QObject *parent) : QSqlQueryModel (parent)
{

}

QVariant PrintFormatModel::data(const QModelIndex &index, int role) const
{
    int columnId = role - Qt::UserRole - 1;
    // Создаём индекс с помощью новоиспечённого ID колонки
    QModelIndex modelIndex = this->index(index.row(), columnId);

    /* И с помощью уже метода data() базового класса
     * вытаскиваем данные для таблицы из модели
     * */
    return QSqlQueryModel::data(modelIndex, Qt::DisplayRole);
}

QVariantMap PrintFormatModel::get(int idx) const
{
    QVariantMap map;
    foreach(int k, roleNames().keys()) {
        map[roleNames().value(k)] = data(index(idx, 0), k);
    }
    return map;
}

QHash<int, QByteArray> PrintFormatModel::roleNames() const
{
    QHash<int, QByteArray> roles;
    roles[idRole]="id";
    roles[productIdColumn]="product_id";
    roles[printFormatId]="print_format_id";
    roles[x1]="x1";
    roles[y1]="y1";
    roles[fontSize]="font_size";
    roles[printFormatKey]="print_format_key";
    roles[printFormatText]="print_format_text";
    roles[boolPrintFormatKey1]="bool_print_format_key_1";
    roles[boolPrintFormatKey2]="bool_print_format_key_2";
    roles[boolPrintFormatKey3]="bool_print_format_key_3";
    roles[boolPrintFormatKey4]="bool_print_format_key_4";
    roles[boolPrintFormatKey1Text]="bool_print_format_key_4_text";
    return roles;
}

void PrintFormatModel::setId(int idNumber)
{
    productId = idNumber;
}

void PrintFormatModel::updateModel(int id)
{
    this->setQuery("select id, product_id, print_format_id, x1, y1, font_size, print_format_key,"
                   " print_format_text, bool_print_format_key_1, bool_print_format_key_2,"
                   " bool_print_format_key_3, bool_print_format_key_4, bool_print_format_key_4_text"
                   " from ProductConfigForPrint WHERE product_id = " + QString::number(id));
}

int PrintFormatModel::getId(int row)
{
    return this->data(this->index(row, 0), idRole).toInt();
}

It's explained in the Using C++ Models with Qt Quick Views chapter of Qt's documentation.