This has made me wonder even more about a mirage my family saw about 30 years ago. It was after lunch on a clear Summer day, at Port Elliot in South Australia. We went outside where there was a wide view of the bay. Far out to sea, we all saw a mirage of a small desert island with palm trees and what looked like buildings. (Image of an approximation of the mirage attached. The buildings were more complicated, but still sandy-coloured and squarish.) We stood there looking at it for at least 10 minutes, maybe longer, then the adults said we should all have a nap, as they were feeling a bit bewildered. I've always felt a bit disappointed I didn't get to watch it disappear.
I checked with my mother today, and she remembers it the same way I do. She told me she had been discussing it a few months ago with her cousin and her cousin's family who were there with us too, and they still remember seeing the same thing.
There are no such islands, either in that direction, or further out to sea, and as far as we know there are none like it anywhere near the southern coast of Australia. It was not foggy. I remember it as a very clear, sunny day, but it's possible there may have been some clouds.
I've done a bit of googling, but can't find anything that describes such a mirage. It does not seem that it could be a Fata Morgana. Perhaps Meffy, or someone else with knowledge of atmospheric optical phenomena might be able to explain it for me.