Definitely tell your landlord. Google will show your address over time under the business name anyway. Our landlord was fine when we used to run our own business at our rental, he'd been running his own business for years and had lots of advice.

Good on you for having a crack. There are many home-based beauty businesses around our area and they are killing it. I guess it comes down to the old, "it is only illegal if you get caught" scenario. For me, I would suggest setting everything up properly from the start. It might take a little bit of work and a few bucks in investment but it will be worth it in the long run for sure. You can set up as a sole trader and get an ABN (online). You don't have to register for GST until you have an annual turnover of $75,000 or more. You can still choose to register for GST if you want. I would probably let your landlord know, just out of respect, if nothing else. It could make for an awkward conversation at inspection otherwise. I would HIGHLY suggest Professional Indemnity insurance for your industry. You need to plan for your WORST possible customer scenario and hope for the best. You can register the business name online too. As soon as you can, get yourself an EFTPOS option, being cash only is super annoying for customers and will limit those that will choose you. You can speak to your bank about a terminal or you can use a company called Square. The fees are a major pain but worth it, IMHO. Start advertising on Facebook, be really awesome to work with, concentrate and work hard and you will be booked out before you know it.

This is a handy guide
https://www.business.gov.au/guide/starting

Yes you need to pay tax, register an abn and business trading name. You don’t have to tell landlord and download and make an account on schedule it is a free sailing equipment and does all bookings and appointments as well as tax and sales reports. I use this myself