It's been a while since I was an active freelance writer for magazines. I now concentrarte on the more lucrative corporate communications market. But, having said that, I offer the following advice.
In 'my day', I would either discuss or submit a piece to a magazine and then negotiate the rights and the payment in advance of publication.
In those days, which weren't that long ago, I would then receive payment and would be responsible for paying tax on that at my end. More recently, publications have been taking tax out of the final payment unless the writer had a registered business.
My advice to you would be a combination of the above:
1. Discuss an article or simply submit it to a magazine and follow-up the Editor soon after.
2. Negotiate the rights and the payment rate.
3. Submit an invoice, as confirmation of your agreement.
And, as part of that final point, it's wise to register a business name as well as an ABN. For one, it tell you (and the world) you're professional, and you'll also gain the full use of your money and be responsible for your own tax.