Podocarps can have surprisingly broad short almond-shaped leaves. And aren't seen very much around here, so we aren't familiar with them. But this does not look like any podocarp I've seen, the leaves don't sit on the branches correctly to start with. Another coniferous objection was to resprouting, which certainly cypresses and pines don't do. But there are some conifers that do resprout from bare wood if you cut them back, there was one in my garden which resprouted even from the stump which I reduced it to for removal, I think it was a cryptomeria of some kind. But this is not anything like that either. The leaves look like broadleaf to me.

Having googled some close-up shots of L. pileata, which is what I first thought of too, I'm not convinced it is that.

Someone mentioned Baeckia (correct spelling), which is a member of the Myrtaceae, like many Australian plants. I think it is quite a reasonable suggestion. There's a picture of B. camphorata on wikipedia which has just the right jizz in terms of the way the stems hold themselves and the branching. The leaves don't look spot on, but there's about 50 species in the genus, so maybe another one, but it seems tricky getting pictures for comparison.