It seems you live in Australia, I do too. Personally I would not take a little pet bird like a cockatiel outside, there are just too many predatory birds out there, many more in addition to the ones you mentioned. I once took my purple crowned lorikeet outside many many (MANY!) years ago, because we had a very small bottlebrush plant in a pot and i thought he'd enjoy the flowers. Well, a magpie that I had not seen certainly saw him, and swooped in and almost got him, even though I was standing *right there*!! I would never have forgiven myself if anything awful had happened to my sweet little lory.
Predatory birds have SUCH sharp eyes, can be quite fearless if they're hungry enough, and you won't see them but they will most definitely see your bird. You certainly could harness train your bird, it may be a useful thing in some situations for you, but I think your wider question is whether it's safe to take your bird outside in one. A harness will not provide any protection from a determined magpie, butcherbird, kookaburra or currawong, etc etc etc, and in my opinion it's just not worth the risk with a little bird like a cockatiel in our environment in Australia.