Matt,
Welcome to pprune.
The first thing you need is to get your father’s Record of Service, obtainable through the Veterans Agency.
Your father 147744 was awarded the DFC on 11 Feb 44. I did not find a citation and this might suggest that it was a ‘non immediate’ award, possibly at the end of his tour. You might want to employ a National Archives (NA) researcher and he will be able to acquire (for a fee) the squadron’s RAF Forms 540 and 541 (the squadron diary and record of sorties flown).
Is there a reason why you don’t have your father’s logbook or medals and besides the DFC, he will have at least 3 others: Defence Medal, War Medal and Aircrew Europe Star.
Hope this gats you started but – FIRST The Record of Service!
Old Duffer