Before offering to db, I put debug printing:
qDebug() << "db.drivers()=" << db.drivers();
It gives correct list of drivers on the development platform and empty set on deployment platform.
if (db.isDriverAvailable("QODBC"))
db = QSqlDatabase::addDatabase("QODBC");
//It is a fragment of code for opening mdb (str is a full name to file from file-open dialog):
if (db.isOpen())
db.close();
qDebug() << "db.drivers()=" << db.drivers();
db.setDatabaseName("DRIVER={Microsoft Access Driver (*.mdb)};FIL={MS Access};DBQ="+str+"; Uid=Admin; Pwd=; ExtendedAnsiSQL=1;");
bool ok = db.open();
if (ok)
{
// processing with sql
}