Drawl

Southern drawl is how we characterize the dialect of English used in the American South.

http://www.englishbaby.com/vocab/word/13471/southern-drawl

As you said, people who speak with a drawl tend to speak more slowly and prolong their vowel sounds. For example, short words like “they” will sound much longer when spoken by someone using a southern drawl. There are also certain words that belong to this dialect, such as “y’all,” which means “you all.”

Best,

Amy

Since I don’t live in Australia (and have never visited), I’m unfortunately unable to answer your question about whether the Australian dialect is similar to a southern drawl. 

As far as learning the southern drawl accent, I would recommend watching movies that are set in the American South. The characters will likely speak with a drawl, which is probably the most authentic exposure you can have to this dialect.

However, unless you are planning on moving to the American South or expecting to be in contact with people from there, spending lots of time analyzing this type of speech is not important to understanding English as a whole. 

Best,

Amy

The movie The Help (2011) is set in the South and should include examples of the southern drawl. Additionally, classics like Gone with the Wind (1939) also showcase this kind of speech. Feel free to Google movies made in the South! You’ll find many options.

Best,

Amy