Agree with Soulman, as you're in Aus where it's a lot hotter than over here in the UK - the bat is more likely to lose the moisture within the bat and therefore become brittle and prone to breaking. By applying oil, you create a seal around the bat that stops the moisture from escaping, but this will eventually evaporate - so you need to re-apply a light coating of oil.
You can normally feel if a bat needs an oil by if it feels dry and I seem to remember your bat having a scuff sheet on it right? So if it needs an oil, just give it a light coating everywhere the willow is exposed (not covered by stickers/scuff sheet/toe guard) - but not on the splice or too close to the join of the bat and splice.