Do Australian airports issue tourist visas on arrival to EU citizens, or does one need to get a visa beforehand from an embassy abroad?

Have a look at this site, if no one else can answer your question this has all the details.

http://www.immi.gov.au/visawizard/

I believe that you need to arrange your visa first....

Certain passport holders can get an E visitor visa......most EU countries are eligible, but you need to check this first

http://www.immi.gov.au/visitors/tourist/976/eligibility.htm