Where can I find guided tours of Australia by Aboriginal persons, or organisations, ideally where profits go back into helping or preserving the local people and/or landmarks? I would love to see Ayers Rock.
Many "Aboriginal tours" and "Aboriginal experiences" exist but, while you will have Aborginal guides, in many cases these operations are not majority or even largely operated or owned by 'Aboriginal persons' - some care will be needed in discerning which are 'authentic' in this respect.
Mild warning: You are probably aware that the subject of the rights and relationships of the Australian Aboriginal peoples has been and remains a much debated one, with a turbulent history, and you will still find strong opinion and sometimes unreasonable bias at either extreme of the opinion range. You are unlikely to come to too much harm in Australia if you express opinions or make related requests from any perspective, but you can expect the possibility of abuse or rude words from people of either persuasion if you behave insensitively.
A good start?: One operation which appears at face value to meet your criteria is Aboriginal Cultural Tours, South Australia apparently owned and operated by Quenten Agius. If Quenten's organisation does prove to meet your criteria he is probably a good source of infomation of similar origanisations in other areas.
The following is NOT intended to be a direct answer to the question but has direct pertinence to underlying issues.
Several comments have been made above re the use of the names "Uluru" and "Ayers's Rock" for the edifice whose official name is "Uluru / Ayers Rock" (no apostrophe). Issues relating to the naming of the rock are intimately entwined with the issues of the rights of the Australian Aboriginal peoples and every aspect of their existence and relationships to other Australian residents and to the land. The name used, who by, and when, as touched on very briefly in the comments, is of relevance to Mykael's request. If what Simon says is correct it seems that the majority of the population in the UK have not 'moved with the times'.
As a small insight (make of it what you will) the following is based on Google's NGram reporting of the use of the the terms "Uluru", "Ayer's Rock" and "Ayers Rock". Whatever else it tells us, it seems that apostrophical' correctitude is fighting a losing battle in this case :-).
Use of the terms shown in reference source "lots of books" 1920 to 2005. (Ignore spurious 1880 at far left)
From Cultural Survival organisation.
Tjapukai - Aboriginal Cultural Park - note that the ownership or operating body of this 'attraction' is not clear.
Very pretty Tjaupukai glossy brochure - owenership still not clear.
Tjapukai FAcebook page - underlying management and structure still not clear. Either these people are VERY laid back OR something is becoming clear.
Responsible Travel Aboriginal Tours - NOT exactly what you asked for BUT may be of value
Perth Aboriginal Tours - lacks obvious up front ethnic buy in.
There are many Aboriginal owned and operated tours throughout Australia, and also those who work closely with Indigenous operators who are non indigenous owned tour operators such as myself Adventure North Australia and The Bama Way Aboriginal Tours. We work with 3 Aboriginal owned and operated tours in Tropical North Queensland.
Look up the Indigenous Tourism Champions which will give you the tours operating throughout Australia.