Again, hard to pin down ... I have a similar chest my grandfather made in the 1930s, but there is nothing to say yours is not earlier.

Is it local wood? Or an immigrant piece?

It looks like the tops and sides are single planks, which often indicates earlier pieces.

Are there any saw , plane or chisel marks that might help date it?

Notice how similar yours is to this English chest. Other features such as hinges, lock and till will tell us more about your chest, BTW it has beautiful handcut dovetails.

Yes...look at the differences too....notice how the dovetails on the English piece are closer together...notice that the English piece has a shaped edge on the top. Notice the way the "frame" around the top fits at the corners.
I don't think the OP's chest is "old" I think it's an Asian repro.
Pictures of the inside and the bottom and the hinges will tell more.

Definitely not an Asian repro as I have the provenance from around 60 years ago.

It was owned by a well known antique restoration specialist before he passed this year.

60 years ago...or a little less puts it about the post war time when the Asian imports were coming into this country....many brought back by service men who were stationed in Japan, Okinawa, the Phillipines or other places in Asia.
Many service men were stationed for long periods and brought their familys. One of my good college friends went to highschool in Okinawa, because her father was stationed there.

Yes Linda, but the OP said "Australian", so I don't think that applies. Few if any Aussies were in the occupation forces.

Didn't notice that.....
Was also going to say that the type of wood would tell a lot....but maybe not in Australia.

How big is it and is each side a single plank? We have one that's pre-Civil War with provenance (family) but the hardware is later because it was a utility piece kept in the barn or shed.

I also have a family blanket chest that is pre civil war....and the top is planked up. has no handles and sadly has been painted, and painted....and painted!

I think though, that single board pieces tend to be older because wide old growth was available. They also made pieces out of glued up narrow boards, so that doesn't mean it's not old...but a newer utilitarian piece would be less and less likely to be single wide boards in American species. The boards on our chest are close to two feet in width.