The simple answer is that you can get into consultancy with your background.
The more complicated answer is that there are many types of consultancy, some will be much easier to get into than others and, depending on where your interest really lies, some might be not at all what you are looking for.
You need to approach this in a very structured fashion, with plans and fall-backs in place. Given that you have five years clinical experience (and presumably a post-grad exam?), adding more clinical experience will not help you. Therefore, if you are genuinely going to leave, you should do so asap.
I think you should consider a few questions in more detail:
1) What type of consulting? "Strategy houses", Big 4, Niche etc
2) What type of client? The NHS, private companies, big pharma vs biotech vs start-ups, healthcare services, a range of all the above?
3) Location - are you going to stay in Sydney or are you moving to the UK? Being in the UK would be easier for sure. For example BCG had an information evening in London a few weeks ago for doctors looking to move to consultancy. Anywhere else? The US?
4) Other options - what else would you like to do? Which easier steps might make a move to your ideal role more feasible with a year or two of non-medical experience? The market research firm doesn't sound ideal, but there may be other options that you can do more quickly that will improve your CV. Is business school a possibility? If not, why not?
If I was in your shoes I would do the following
1) Identify the companies I am interested in and find out as much about them as I can
2) Find doctors that work for them - eg on LinkedIn - and approach them for advice, preferably using an email such as doctors.net
3) Ensure my CV and cover letter are as good as they can be and then apply
4) Work out what I am going to do if that doesn't work out. Consider the pharma industry, healthcare service providers, other types of consultancy, business school etc
5) Find doctors that work in other areas or that have gone to business school, and talk to them
6) Keep repeating until you have an offer that is either ideal, or at least something that you can see as a better option than staying in medicine
7) Go from there
8) Expect the whole process to take months, if not years, and make sure you don't derail your current career while you are doing this.
Certainly I would look seriously at the McKinsey positions advertised on this site, with the proviso that you are prepared to work as a management consultant to the NHS. Even if you end up hating it you will have plenty of options subsequently.
Not sure how much help that is. Your questions are very open so it is difficult to answer in a specific fashion. For what it's worth, many people have made this move and they aren't that hard to find. If you have more specific questions, post away.