Well, the easiest place to get a proper, legal work permit for you as an Aussie is the UK. We have a 'Working Holiday Visa' for Australians, New Zealanders, Canadians and Japanese citizens who are between 18-30 years old, but you'll need to have £1600 in your bank account before you come. This is a fairly reasonable requirement and should set you up for at least a couple of months during which time you can look for work.
London bars are full of Australian staff - in fact it's pretty much impossible to go anywhere in the capital without hearing an Aussie accent but London is quite expensive - think Brisbane/Canberra prices. Edinburgh and Glasgow are also very popular with people on these visas and Australians do seem to be able to get bar work, and in the high-end places, reasonably easily.
In the Summer there is tonnes of work, even with the current economic climate, for crop picking, general farm work etc. but the pay is, as you probably guessed, quite poor. There are lots of temp. job agencies which will place you doing warehouse work, that kind of thing.
Mainland Europe is quite depressed - Spain, for example, has a 25% unemployment figure at the moment and you will find it tough, especially as a non-native, to get work doing anything. Scandinavia seems to be riding the storm pretty well, but they don't have the work visas for foreigners that the UK does.
To set yourself up for a long stay, I would recommend basing yourself in the UK. Bring as much money as you can and use what work you can find to stretch it out. You will find it easy to rent a room in a shared house for reasonable prices or, if you're up for the outdoors life, a large tent and a motorcycle or cheap car will keep you mobile, especially during the summer. Not recommended for the winter!
From the UK, it's a cheap trip to France and the rest of Europe is yours, but as a non-EU citizen it will be tough for you to get work and it will most likely be illegal. If you want to travel Europe cheaply, I'm sure there's still a Europe-wide train pass and it's by far the best way to do it on a budget. The UK train system is a shambles but once you hit mainland Europe they're superb.
Sadly, I don't think your degree will help too much, but you could try hunting around for small, local newspapers that might be interested in offering you something. I think it's doubtful, but I don't know the industry at all.
I'm just wondering if you might be able to make something out of a blog or website (given your skills), documenting your travels and advising other Australians on how to do what you're doing. I'd bet most of the sites that do this already are pretty amateurish or out of date with respect to the European recession. If you write it well and know how to publicise it, you may be able to make some ad-type revenue, maybe even an e-book or similar but I wouldn't bank on it!
That's about all I can think of.
Good luck!