Be VERY CAREFUL with farmers in Australia. They will cheat you on money, and have a well deserved reputation as opportunistic rapists.
Ask An Australian
Be very careful who you're tarring with that brush :(
You can get a license without citizenship. You just need a permanent address
I think you'll find many farmers will have a car pooling system or will be willing to organise one for you to get you there.
Backpackers accommodation also have people ready and willing to car pool in the small towns.
Keep in mind many Aussie farmers will cheat you, if you happen to find a good one please look after them.
App idea: Glassdoor for backpackers to rate farmers
If farmers doing the right thing get rewarded with a steady stream of workers, and the shonky ones couldn't get them, the power goes back to the backpackers.
That almost exists with things like helpex already. I'm not sure if there's some variant for paid work. My parents have a farm and have had a bunch of backpackers stay. Some of them definitely did have some stories about being cheated etc.
However, it's a bit different to what op is looking for as it's just a bit of work for food and accommodation, as opposed to full days of work for pay.
On the whole I think the majority do the right thing, but there are definitely enough that are dodgy to create a bad reputation