I dont know your personal situation, but you seem reasonably intelligent from your write up so ill try and give you some advice. if you really want to work and earn a living I dont see why this wont work.
get yourself an ABN as a sole trader. this is free and takes minimal time.
Go and buy/lend a secondhand lawnmower, line trimmer, pruners, gloves, some basic hand tools and garden tools. this is gonna cost about $200-$400, if you dont have it handy save up, borrow from someone, bullshit the job agency tell them you have a job lined up and need supply's, sell scrap metal. there's a heap of shit you can do to get the cash to start up if you are truly motivated.
make up a flyer "Dolebludgings home and yard maintenance" put your abn on it put what service you can provide on it put your phone number on it all that shit, go to the job agency print a heap of these out. post them up on the shopping centre public notice boards.
try going to your local real estate agents and offer your services to them, they constantly have tenants moving in and out of rental propertys and need to have these properties maintained, give them a flyer tell them "if you need help please give me a go"
post an ad on your local facebook classifieds (every suburb has one) same shit offer your services and ask for a go, pensioners need there lawns mowed and cant physically do it anymore they have $$.
centre link will not cut you off until you earn a certain amount of money you have an extra form to fill out that's it. (reporting business income form or something).
Thats really all there is too it I cant tell you how much to charge per hour cause it depends on the demand, keep a monthly logs of all expenses and income keep receipts you claim all that stuff at tax time, offer free estimates with no obligation.
Anyone can do this all it takes is hard work and motivation.