While I'm not an Airbnb host, I have had a lodger in my front room since July of last year, and mindful of my obligation to alert my insurers of any material change to the property they were insuring (and bracing myself for some increase in my premium) I popped into the local office.
The woman on the counter asked me if I had formally leased the room to my lodger, and I said no. She asked if the arrangement could be characterised as being "like Airbnb", because if it could they (my insurers) "didn't want to know about it". I swiftly decided my arrangement was indeed "like Airbnb"!
I also contacted my local Revenue Office in case I was liable for Land Tax. Once again, the news was good. So long as I wasn't renting out a granny flat (or any part of the house with self-contained amenities including cooking facilities), so long as I kept "bumping into my lodger in the kitchen", I would not be liable for Land Tax. It seems pretty clear this would apply to Airbnb as well.
I did get some bad news from the ATO, though. I had spent a bit of money repairing the front room to make it fit for habitation, and I assumed this would be deductible from the rental income. No such luck – repairs are only deductible if you are repairing damage (or wear and tear over a reasonable length of time) attributable to the lodger/tenant. What I was repairing was damage done (by a leaking roof, mostly) while the room was not being let out (or available for letting), and thus the costs of those repairs were not deductible.
On the other hand, the new carpet I had laid in the front room could be depreciated, that is, I could get a percentage of its cost deducted from my taxable income each year over its life. The same applied to new furniture, appliances etc acquired for the common areas shared with my lodger, but only the percentage attributable to his share, so a percentage of a percentage.
A couple of useful PDFs can be downloaded from the ATO site – I'd give you the links, but Choice bounces posts with links embedded!