Yes, there were wars between Aboriginal Australians. We have some evidence for this:
1) The existence of wooden shields. Shields only exist in order to block the weapons of others, and do not have utility for hunting (unlike knives and clubs), so therefore demonstrate that fighting was taking place.
2) Australian rock art dating back at least 10,000 years depicts fighting scenes using weaponry.
3) Research by anthropologists since the mid-19th century has witnessed wars between Aboriginal Australian tribes. Not only did wars take place over hunting territory or ownership of wells, but also over the abduction of women.
These conflicts between tribes often resulted in long-running feuds, as a result of 'payback law', whereby a raid will cause retaliation from the other tribe. These could be devastating - anthropologist T.G.H. Strelow witnessed a three year conflict that killed 20% of the population of the tribes conducting the war.
I am no anthropologist myself, so you might get a better response from
/r/Anthropology, but as far as I understand it, Aboriginal Australian tribes did not structure themselves in such a way that would result in a kings/lords/subjects relationship, and war was not fought for these reasons. Aboriginal Australian tribes were led by the elders of the group, and they fought to defend/gain hunting land/access to water/women, not to subjugate other people. But as I say
/r/Anthropology may know better than me.
Source: Azar Gat
War in Human Civilization, pp. 17-25