Great Danes normally have quite a low prey drive, which makes most of them not a very desirable hunting dog.
My 5 year old Dane, Savage, despite his name, is generally very gentle with humans and animals alike. I've seen him in a few fights with another male dog, but if he sees a deer, for example, he will chase it a few yards, then lose interest.
A few years ago I began taking him grouse hunting with me. Surprisingly, he will retrieve a shot grouse, but I think he's doing it more to get my attention than anything super instinctual (though I could be wrong). Doesn't even want to eat them, even though I raise him on a raw diet (mostly chicken).
On the other hand, he pretty much ignores my neighbor's free ranging chickens, and just wants to play with the baby and adult goats. When he hears wolves howling near our place he might bark at the sound a bit, then go back to being his normal lazy self.
Your Olive seems much more promising than Savage, but don't be disappointed if she never really "gets" it like your greyhound (whose sight-hunting skills were bred right into him from the beginning til today).
Just my opinion.
