When you lift the lid off the range of different uniforms available to Australian colonial forces it is quite amazing. I must admit I had no idea of the variety. Pre-federation when Australia existed as a series of States under British rule there was a lot of competition between them to 'outdo' each other, and this was reflected in uniform. The Australian detatment that made it to the Sudan in 1885 was actually a New South Wales unit of infantry and artillery.
Although we can probably (and from everyones replies) fairly shrewdly deduce what what worn in the field, it would be interesting to look also at what could have been worn in the field. The slouch hat apparently had been in military use since 1885 when it was introduced for the Victorian mounted rifles:

When it was first introduced it was worn with the turn up on the right:

Although I have found no pictures of slouch hats in the Sudan, I have read reports that soldiers hated the pith helmets they were issued with in the Boer war (which is where they are commonly assumed to have begun use) and used their pith helmets as footballs until they were re-issued with the slouchies. Their use was certainly widespread into the 1890's according to the digger history website.
So I could see a unit of Aussies bored on outpost duty in the Sudan, having a game of football or cricket in their casuals..some of them in slouchies...(I know I'll be shot down in flames for this..) when the Mahdists make a sneak attack.
This is a good site to have a look at:
http://www.diggerhistory.info/pages-uniforms/slouch_hat.htm