(Transcript from World News Australia Radio)
A referendum on the issue is now being proposed for 2015.
The new date was set after the federal government shelved an earlier aim to hold the referendum this year.
Advocates say the inquiry is important step in raising awareness of the issue, but that there's still a long way to go to win enough community support.
In an initial step towards Constitutional recognition for Indigenous people, the Federal Government introduced an Act of Recognition Bill in Parliament last September.
That would express broad political support for a referendum on the proposal in 2015, with the specific timing and wording to be worked out later.
The first task of the Parliamentary Committee inquiry is to try to ensure that the Act of Recognition Bill is passed when debate on it resumes next month.
One speaker at the first public hearings of the committee was Tanya Hosch from the group, Recognise, which is working with Reconciliation Australia on an awareness campaign.
"Those levels of awareness will go up and down for a while until we start to build further momentum. But I think it is worth pointing out that our team which has only been in place six months has already gathered over 125.000 supporters to the movement and we're confident that will continue to grow."
Tanya Hosch says advocates of the proposal are pleased with indications of support from the major political parties.
But she agrees there's a long way to go to win the support of voters.
"You definitely need to have reasonable levels of awareness across the country to have a chance of success. The political leadership and the cross party support for this activity is critical and so I guess that's one of the reasons why we're feeling excited about the potential passing of this Act in a couple of weeks time and I'm feeling really positive about that and then we've got the funding activities. But it's going to be a multi-pronged approach I guess with community awareness raising all the way through. We're going to continue to look for opportunities for social media in particular to engage people and keep them informed."
Independent MP Rob Oakeshott, who is on the Parliamentary Committee, says bipartisan support beyond the Act of Recognition Bill is by no means guaranteed.
"There is some really unfinished business now from political leadership. There is bipartisanship to a point and that point is acceptance of an act of Parliament that basically says we all think this matters. There is still not clear bipartisanship on a detailed question to be put [to the public] and that remains the critical step for Tony Abbott and Julia Gillard and their respective parties to work through. Without that we're going nowhere fast, and we need that soon."
Constitiutional law Professor Anne Twomey at Sydney University says even if the Act of Recognition Bill is passed, the much harder task will be the wording of the proposed referendum question to put to voters.
She says the major parties should be aiming to come up with wording that future generations won't want to change.
"It's one of those things that the devil is always in the detail. And we need to have a much more considered approach as to the terminology of the referendum changes. From my view, the way that I see it, we need to have something that will last for a long time, that is not just a thing for today but that if it's going to be in the constitution for the next 100 years, will stand up to scrutiny in 50 years time, in 70 years time in 100 years time. So that's going to take a fair bit of time to get something of that stature in the constitution."
Tanya Hosch says although Indigenous leaders and the broader Australian community have a daunting task ahead of them, the reward will be worth it.
"I'm not sure that we can say that can definitely will make a lot of difference on a day-to-day basis. But what I do think it will do regardless of what model we end up with, is if we can get that constitutional recognition in place and can get the racially discrimnatory elements dealt with, I think it provides the basis of honest conversations going forward and that sense of seperation that Aboriginal and Torres Strait Islander people often experience in their own country can start to be corrected and take us forward as Australians in a way that we all want to see happen."