I found a company in Africa that lets you drive if you're under 21.
http://www.driveafrica.co.za/car-rental/under-21.html
Also a forum for travel deals has special sneaky codes to try using if you are under 25 and even under 21. The only sticking point might be the fact you aren't from the US and I think the codes are mostly for use with university and college students. For instance on Thrifty's site they say: "Thrifty Car Rental will rent to government renters under the age of 21 who are on official business." The forum is here
http://www.fatwallet.com/t/63/521905/
Basically the bottom line is that most companies will charge extra but that usually applies to people 21-25, it's hard to find many that rent to under 21. This company in LA does that:
http://www.bnm.com/atwestla.htm
At your age and if you plan on travelling a place for a long time, you might want to consider buying a vehicle. In anycase, you'll need an international driving permit.
http://www.smartraveller.gov.au/tips...g_licence.html