Hi Millemini
Welcome to the Emirates forum. Good to have you on board so please stick around and make yourself at home. There is a wealth of information on the forum to help make the most of your Emirates experience and we are a fairly friendly bunch.
I cant answer your question specifically, but I've had 04:00 departures from DXB before and got an amenity kit. Not too sure what the cut off is but hopefully someone with the SA flights will be able to give a definite answer.
Safe & Happy Travels
S