It seems to me that you are being asked to write a persuasive essay one way or the other? And that you are writing in agreement with the statement?
If that is so then the first response here is most useful to you. Things to look at are not only the history that led to racism, as mentioned above but the two types of racism that exist. Legal racism (segregation laws, Jim Crow, etc) and the racism that is learned and expressed by people. Here you would want to consider the Ku Klux Klan, lynching, church bombings, experiences of the freedom riders, etc.
You will want to contrast how racism existed in Australia at that time. Was is legally ingrained into society? Was it more personal? or both?
Use the evidence to prove your point.
I agree with Post 3. Comparing the histories of Australian and American treatment of indigenous peoples would be much more historically appropriate. In any case, I hesitate to attach the sort of value judgement this question seems to suggest. Racism was present in both societies, and I do not think we can objectively say which was better and which was worse. Rather we could examine the racial assumptions, material conditions, and political backdrops behind the racism in each country to yield conclusions about the development of institutional racism.
The fact that Australia was a "convict dumping place" has nothing to do with racism. Racism in Australian history comes with regard to Australian treatment of aborigines. I would argue that Australian racism was worse because African Americans in the US in the time you are talking never had children taken away from them to be raised by white people in hopes of assimilating them into the mainstream culture.
Of course, what you should really compare is Australian treatment of aborigines and American treatment of Native Americans. This is the true analogy and you would find many more parallels there.
Australia and America have different histories in this respect. Australia was a convict dumping place. America built an economy on slavery. After the end of slavery in America, there was a deeply rooted racism because of slavery. Americans made themselves believe that blacks were inferior and not human for so long, they could not just back off and change the view completely.