Organising a trip to Australia requires a certain degree of administrative preparation, which you should not neglect. There's nothing insurmountable, but it has to be done.
If your trip to Australia is for 3 months or less you will need a visitor visa. Your passport should be valid for the proposed duration of your stay.. If you are transiting another country on your way to or from Australia, make sure you check the entry requirements for that country. Many countries will only permit entry if you have at least 6 months validity remaining on your passport. The Australian authorities have confirmed they will accept British passports extended by 12 months by British Embassies and Consulates under additional measures put in place in mid-2014. However if you plan to work and stay for more than 3 months, you will need a working holiday visa An Electronic Travel Authority - ETA (subclass 601), which is what you need for a stay of less than three months is free of charge. However, there is a 20 AUD service charge if you apply online. There is stacks of information on the Australian Department of Immigration and Border Protection's website www.border.gov.au/Trav/Visa-1. The cost of visas varies according to which type you apply for. There may be a surcharge if you pay for your visa online using a credit or debit card. The ETA is valid for 12 months. Don't forget that you'll need to present a return plane ticket to get your visa.
You don't need any special vaccinations, unless you're travelling via a country where yellow fever is a problem. The country has no hygiene problems, just make sure you're up to date with the vaccinations required in your home country.
If you're planning to hire a car when you're there, the companies will ask for your British driving licence which is valid as long as you remain a temporary overseas visitor. You must carry your driving licence and passport when driving. Make sure you have sufficient insurance, including if you borrow a car from a friend or relative. Hire car insurance often doesn’t cover driving on unsealed roads; check your policy before you set off.
When you arrive at the airport, you'll soon see that it's not a good idea to mess around with the customs officers. They are very strict and apply the rules to the letter. Whatever you do, don't try to bring in any kind of product of animal or vegetable origin. You can't bring in as much as a single tomato onto Australian territory. As for a pot of pâté or a tin of corned beef...let's not go there. You must either leave such things behind or pay for their decontamination. An expensive mistake, it goes without saying.