Hi tillyh, Sorry I cant think what your Australian tree was, Eucalyptus imediately springs to mind but that is only suitable for very large gardens unless it's pruned heavily down to ground level on a regular basis and in any case it has a quite invaisive root system and can cause problems near buildings.
One Australian small tree/shrub that I would like to recomend though is Eucryphia nymansensis, it's an evergreen and will flower after a few years, but it's well worth the wait as the small white, single rose-like flowers are fragrant and extremely attractive to bees. Good luck. Tbird+