3000 PSI - it is quite feasible to have dual citizenship; here in NZ I can apply for NZ citizenship after three years on a full residence visa - the same (or similar) applies in Oz. Much of the Ozzie population can trace their roots to UK, Ireland, Greece, Italy, etc (ever seen their football team, not many aborigines in there!)
As a Dutchy, I thought you would be aware that about 1/4 of Kiwi's can trace their roots to Holland, and no doubt be able to get a Dutch EU passport and citizenship.