I imagine if you REALLY predator-proof the coop and run, you'll be fine as far as hens go. I would keep the door in the middle of the run as opposed to on the side next to the fence. That way if something does manage to reach through the fence the hens can get inside without having to get close to it? That's what I would think, anyway. I'm not sure what type of wildlife you have in Australia, haha.
That said, I'm not so sure your feed and eggs would be so safe. I imagine that if hens can freely go in and out, snakes and mice / rats probably could too. But a door open all day wouldn't necessarily prevent that either, although it would help at night, when those animals are often active.