There is a curfew, but the carriers can get around it if they pay a "surcharge".
I think the curfew is more aimed at inbound aircraft which fly over the inner suburbs.
I would imagine your flight will depart over the water.
I love the "odd" hours of travel, the relative calm and quiet of airports and cities in early hours....it's like discovering another aspect, another layer of something...and travelling always excites me, I go to buy milk and you seem to see another dozen moreinteresting, and beautiful things.
Then it's always interesting to see the impression of a place in daylight vs the affect it hasupon you in night time..and the people that do the graveyard shifts always seem to have the most incredible stories to tell.
If you can get them, photos of something to capture at night are special shots, if you can get them, seems to be a knack I haven't quite mastered yet.