QR 17 then FR 5568 at Dublin
Doha → Dublin → Rome
Timetable, Dublin time
12:35QR 17 from Doha at the gate
06:30FR 5568 to Rome leaves the gate
17 h 55 apart on the timetable, overnight
FR 5568 leaves 17 h 55 after QR 17 arrives on the timetable: more than half a day, so not a connection we count.