Yes you can buy a car privately with some lenders. Other lenders who specialise in this space will insist you purchase from a car dealer.
WARNING: If you read this website, your chances of getting car finance with bad credit will dramatically improve.
If you do wish to buy privately you can, but you need to be aware of the risks. When you buy off another person, you are buying on an "as is" basis meaning, no returns. The risk for the lender is that your car does break down and you become so fed up with it that you stop making repayments against the vehicle. Buying privately, you will be asked to pay around 28% in interest.
Whereas, statistically buying a car from a dealer has less risk for the financier so you may also get a better rate. Dealers in Australia must provide you with a three month statutory warranty meaning you can take it back to them to get it repaired should something go wrong.
But as mentioned throughout the website, it all comes down to your personal profile. In terms of your stability with home and employment, your recent credit activity as well as the previous adverse credit. Borrowers can often get more money than they think to be able to purchase a car. You might apply for a loan for $3,000 but learn you can afford to pay a loan of $20,000 which means you can purchase a much better car, if not, a brand new one.
The trick is to get approved first, understand what you can afford to borrow up to and the go car shopping. You do not start making any repayments until you have actually signed the finance contract which is after you have found the car. The pre approval process is free.