Q: I would like to start a little business like running errands, light cleaning, washing & ironing, even baking. How do I get it started?

A: In Australia you can get started straight away, just contact the ATO and ask for your ABN and get started.
https://abr.gov.au/For-Business,-Super-f...
But it's useful to do some thinking first. A memorable business name is a good first step. Do a search of the name at ASIC http://asic.gov.au/for-business/register... and if you have thought of a great name that people will easily remember you by, register it, and use that name when you are accepting work. This is usually all worked out in a business plan. If you are not trying to use the business plan to get funds from a bank, the business plan can be simple and just for you, but it is good to ask yourself these simple questions before you go out and start "being a business".
https://www.docdownload.com.au/documents...
Other documents you might need in the future