What kinds of degrees are there in Europe that can be completed in 12-18 months?
I don't know of any 1 year degrees in Europe - maybe somebody else can say something about that - but here is one alternative idea (not sure how feasible some of it is though, I only tried some of this from one European university to another):


Go for a masters degree in economics. It's usually 2 years but 


some universities do a 7 semester bachelor + 3 semester master, so if you can convince them that your bachelor is equivalent to theirs, you might be able to get into a 3 semester i.e. 18 month master.
if you have leftover credits from advanced classes in your bachelor or you can tolerate a heavier workload than most, you might be able to finish a regular 2 year master in 18 month. Ask lots of questions beforehand though, to make sure it's really possible - I almost did this and was right on course for the 18 month master but then I decided to take a side job and did the master in 2 years.
if you ask your current supervisor, he might know a professor in Europe, who will agree to supervise your master thesis together with him. Then you can do your coursework in Europe and get started on the master thesis there but finish it in Sydney.



As you've noticed, a bachelor is not feasible, because it usually takes 3 years. 

Another thing to keep in mind - you didn't say anything about your language skills - is that bachelor level classes and any other entry level degrees you might find are usually taught in the local language. Even on the master level your choices might be limited (or it might not be possible at all) if you can only take classes taught in English.