An EU citizen (that is, one who holds an EU passport) may work in any country of the EU, with temporary exceptions for the new-entrant countries. Your JAA licence is valid in all countries covered by the JAA - which is the EU plus a few others.
Non-EU citizens (such as Australians) have no right to work in the EU, except that they may have ancestral rights to live and work in their country of ancestral origin. That is, if your parents were born in the UK, you may have the right to live and work in the UK, but that does not translate into a right to live and work anywhere else in the EU - until you apply for, and receive, EU nationality. To establish what rights you have, and what further actions you must take, you must contact the embassy of your target EU country in your own nation.
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