I think they were organized as standard Divisions, however, as a corps, they more or less had either 2 or 4 armoured regiments more or less permanently attached as well as significant non-divisional assets. The Australian contingent of the Corps was about 5900 or so, but monashes command in terms of combat strength was about 50% bigger than that.
At Hamel for example, the division committed to the battle was supported by a full british armoured regiment, 45 vehicles, and for the first time had significant maintenence units attached. The tanks and the Infantry trained together for weeks before the battle....something unheard of until that time. There were special mobile (I think motorised) Light Artillery units, attached to the Infantry Brigades follwing thgem for rapid unlimbering so as to hel hold the ground once taken....not sure about the pioneers in the Anzac Corps, but the fighting at Villers Bretonneux would suggest that considerable assault assets were attached to the Australian formations. At Hamel, 4th Australian had about 250 guns supporting it, whereas the normal amount per Div was about a quater of that (including Corps assets and the like. Getting off the discussion point, the French and Americans put a lot of effort into railway guns, which I dont think the Brits did
The biggest problem for the Australians by 1918 was manpower. The country only had a population of 5 million or so, By wars end 367000 men were in the army and of that number 67% had been injured and were unfit for combat. War weariness was setting in and the numbers of volunteers joining were hard pressed to fill the gaps. Australia never introduced any draft for its armed forces in WWI. It was the major political issue of the time, as a referendum on the issue was lost (Australian Government was prohibited by law until after Korea from sending chokos....consripts...."chocolate soldiers" because they melt in any sort of heat) outside the bordersd of Australia, though there was some fancy footwork in the Pacific in WWII.
With regard to the New Zealanders in the Anzac Corps, that substantially true, but not quite. Moreover, not all Australian formations were attached to the newly formed Anzac Corps in 1917.
When the Austrlians transferred their infantry to the Western Front in 1916, thay had actually formed a second corps. Australians and New Zealanders thus formed I II Anzac Corps. There were at first four Australian and 1 NZ Infantry Divs attached, but a fifth Australian Div was formed in 1916. In addition XIII Light Horse regiment gave three squadrons whilst 4th Light Horse hgave two squadrons of Cavalry. The New Zealnders gave their Otago mounted rifles to this special attachment. These assets were used to form the II Cav regiment which was a permanent attachment to the II Anzac. There was another regimentformed by similar stripping out of mounted assets in Egypt. The two Anzac Corps went to France with the equivalent of two Cavalry Regiments attached.
It had been intended that these assets would remain Corps assets, however in practice they were more or less continuously directly attached to the divisional structure.
In 1917 there was a reorganization, as you say. II Anzac Corps was renamed XII British Corps and the New Zealanders, who up to that point been attached to I Anzac Corps, were sent to the XII. The 4th Aus Div, which had been attached to II Anzac Corps were transferred to I Anzac to replace the New Zealanders. The two Cav regiments which had always been a mix of Brit, NZ and Australian formations remained attached to their respective Corps, so there is every possibility New Zealanders were still fighting in the reorganized ANZAC Corps of 1917-18 ANZAC Corps fought for most of its existence with 5 Divcs attached, plus numerous non-divisional attachments that were more or less permanent