If you're interested in startup internships and you're in Melbourne the guys at http://www.tinalleybeta.com.au might be able to set you up somewhere. Other options are to ask around coworking spaces like inspire9 or york butter factory (Melb) or fishburners (sydney).
Keep in mind that Australian employment law is a bit anti-internship: technically you can't contribute to a business' productivity without being characterised as an employee. So unpaid interns are, officially, not a thing here.
Unofficially, who knows where a bit of hustle can get you ;)
non-startups to look into: atlassian, campaign monitor, envato, 99 designs, canva (maybe).
Keep in mind that Australian employment law is a bit anti-internship: technically you can't contribute to a business' productivity without being characterised as an employee. So unpaid interns are, officially, not a thing here.
Unofficially, who knows where a bit of hustle can get you ;)