Finally! I have been looking for those guys for a while now. I have been told more or less where to look in the Australian National Botanic Gardens (ANBG). It turns out that they are actually on the other side of the lawn than I thought... Typical!
The tawny frogmouths (Podargus strigoides) look a little bit like owls and are nocturnal, which means that they snooze during the day. They can be very still and well camouflaged (resembling bits of tree bark) so it's easy to miss one. I have only managed to find one and will definitely try to find the other one (there is a pair at ANBG). I'd love to see chicks! I can only imagine how cute those would be.