The Common Name strikes again! Turpentine trees got their common name from the reddish orange resin which resembles turpentine (that is, the real stuff that comes from trees, rather than mineral turps which you clean your paint brushes with). Unfortunately, there are a few trees which had similar resin.

The Canarium australianum, with a fleshy fruit and a large nut, comes from the Cape York area and is bush tucker.

Syncarpia glomulifera is a NSW tree, probably a bit rare now. Its timber is highly water resistant and was used for boat building. The fruit is attractive to fruit bats.

And then there are Lophostemon suaveolens and Tristania suavelons, both referred to as Swamp Turpentine.

All of these could well have flowers which attract birds and animals.

Have you posted on the Australian Natives section? You might get better information on which tree attracts what wildlife. I can tell you from experience that you really don't need something that attracts a flock of cockatoos.