He doesn't NEED hay if he has access to quality pasture grass. PASTURE is really what horses "need". It's just that most of us don't have enough pasture to sustain our horses' weight, or we don't fertilize it to keep it growing well.
I would go with beet pulp and add a fat supplement like corn oil or rice bran. See if you can get your hands on some probiotics too. They are a digetsive aid that will make sure he's properly digesting and utilizing all of his feed properly. Keep feeding the oats, but just the oats (2-3 lbs dry weight, 1 kg).
Also, make sure he is thoroughly dewormed. I don't know what kind of worms you have to worry about in Australia, but I'd imagine it's the same as us in the USA, or similar. I would deworm him now with a double dose of Pyrantel paste (Strongid, Rotectin P) and Ivermective + praziquantel in 4 weeks (Zimectrin Gold, Equimax).