Great to see these beautiful frogs around the house. Our compost bin is overrun with woodies (it's a great way to breed them through the warmer months) and the local GTFs line up on the top edge every night, and jump in when they have one in their sights. There are three in particular who are very regular visitors, and one is huge, bigger than my hand. We also have a tub half-filled with water, use to soak pot-plants, and they regularly soak in that when they start moving in the evening. I don't know where each of them spends the day, but it's at least 20m from the compost bin, so they know their way around quite large territories, and are very regular in their movements.
Just a hint about breeding woodies in your compost - I don't have a lid on the bin, and I don't disturb it by mixing or turning over at all. All I do is add a few cm of dry leaves every couple of weeks to cover the kitchen scraps and to give the woodies some cover. When I want to harvest some, I just grab some handfuls of leaves and drop them into a bucket, woodies and all. They'll breed into plague proportions during the summer - then you'll have to keep the kookas out!
Needless to say, this has been going for a couple of years now and I am reluctant to disturb the thing to get any compost - it's too valuable as a cockroach source.
Jamie