Having a governmental fund dedicated to medical research, and attempting unburden primary care facilities which are getting more and more overstretched every day are the ultimate aims of the $7 copayment for GP visits, and they're both noble, economically viable pursuits. But there are fundamental flaws with the policy that will harm Austrlaia more than it helps it.
The policy as it stands fails to mitigate the increasing rates of hospitalisation and decreasing prosperity bound to occur due to later presentations of disease, at worse stages. A night in hospital costs 100x more than that $7, an average stay including labour and treatment costs nearly $5,000 dollars , and people, most likely those of lower socio-economic status (who are already more likely to be unhealthy, for a variety of reasons) will most affected. Sicker patients don't only incur a treatment cost - they also lead to a less productive economy. These numbers are only a fraction of the real price of this policy.
European Journal of Health Economy research on similar policies (all reliable case studies, done on large sample populations) found that co-payments at primary care facilities do save medical expenditure (so it does achieve that prospect) by imposing a moral barrier to getting treatment, more than a major financial one. The average citizen wouldn't shy away from seeing the doctors when necessary, but the burden was found to be placed on those who couldn't afford it - those of a lower socio-economic status. Increased hospitalisations not only costs the economy billions per year, but also renders the projected income of the co-payment scheme moot. The assumption that because a majority of GP facilities are done on blood pressure monitoring, cholesterol check-ups, and other cases of national priority, and therefore these visits must be good is dubious - I'm not saying it's unnecessary, it's definitely good that people are seeing their doctors about these issues - but these visits or check-ups often don't require long GP consultations in the first place, something I'll expand on below.
Another, less dangerous way to go about reducing the burden on GPs:The suggestion, brought to me by a trained GP who works in regional Sydney, that we should impose a fee after a certain threshhold of visits are reached of between 4 - 10 a year, with exemptions made for those who NEED regular appointments, like rural cancer patients, is a fair one. Most patients visiting GPs in that region are older, coming in for routine check-ups, or those seeking secondary appointments for discussing results. A lot of these GP visits are unnecessary, especially when you consider a lot of this monitoring can be done through aged care facilities, or from nurses stationed at GP practices or hospitals, and reported to doctors for further treatment or follow up, if required.
A system like the one she's proposing will raise some funds to go into the research budget while also reducing the burden/waiting times in primary care facilities better, but there are better measures out there to improve primary care and reduce the burden on the economy.
Other ways of Reducing the Burden of Healthcare:One big saving would be to better negotiate commonly prescribed medications. Currently - in Australia, medicines are negotiated through collective bargaining, rather than to individual hospitals as is done in the US (a big reason why their health system is overburdened), but is not done efficiently, and savings to the tune of $1.3billion  can be made by better negotiations.
Also a bigger focus on preventative health, and getting GPs to give patients long term, self management goals, which only occurs in 57% of the time , will improve health outcomes for patient and save the primary care system more visits too. The low rate of this occurring at the moment indicates a benefit in emphasising and advocating self management plans in the educating of existing and emerging GPs.
And increasing preventative services will reduce the burden on the healthcare system, something I talked about before in this post about how doctors think, and how they need to embrace, rather than scorn preventative health and explained in the case of cancer in my cancer council essay competition entry. I'll further explain other ways in which preventative health will reduce the burden on healthcare in a future post dedicated to that topic - likely after I finish and publish my paper on the pharmaceutical industry (so do subscribe/follow if you're interested).
Getting nurses to handle some care or possibly some form of letter sending by GPs (phone calls can't be made for confidentiality reasons) to confirm results of blood tests and x-rays that don't indicate/require follow up will also lead to less unnecessary consultations, without endangering patients.
To summarise:Overall - with the way this policy is being implemented now - I oppose this measure. It will cost more than it saves, and leaves a less healthy population (remember - less healthy people = less healthy workers = less healthy economy). There is a need to streamline and reduce the burden on primary care, and a need for more research (which should be seen as an investment rather than a cost, something I talk about here), but this is not the way to go about it.
However, we have it now, and we have a year to fix and improve it before it becomes effective in July 2015. Hopefully, some changes will be made to make this a more effective, safe policy.
 Australian Department of Health publication, Quarterly Medicare Statistics, 2007 - 2014, http://health.gov.au/internet/main/publishing.nsf/Content/Quarterly-Medicare-Statistics
 AIHW, Admitted Patient Care: An Overview 2010 -2011
[a] Six dollar to see a doctor: a GP’s view,
 A Kill, K. Houlbourge, How does copayment for health care services affect demand, health and redistribution? A systematic review of the empirical evidence from 1990 to 2011. Eur J Health Econ. 2013 Aug 29. http://www.ncbi.nlm.nih.gov/pubmed/23989938
 WB Runcimen et al, CareTrack: assessing the appropriateness of health care delivery in Australia., Medical Journal of Australia 2012 Jul 16;197(2):100-5. http://www.ncbi.nlm.nih.gov/pubmed/22794056