As I say, I'm not familiar with the rules in Aus. Here in the USA, you're doing business, or your not. If you're doing work for someone and asking for payment, that's a business, and along with it comes such things as licenses and paying taxes. That's the routine. Not that people don't do it without paying their taxes, that's called "tax evasion"
A contract is so that you *don't* end up talking to the lawyers. It sets down the agreement between you on paper (or electronic paper) that seals the agreement. It doesn't require a fax, if you have email. If I may say, it's naive for either to go into this with an assumption that there won't be a contract and that everyone will just be happy with the deliverable and the associated fee.