This is quite interesting, as it has long been the popular belief that birds were responsible for migrating fish eggs to new bodies of water (albeit usually stated as external transport on legs and or feathers, not internal). Even Charles Darwin proposed this explanation. But there has been little scientific evidence that this was actually true.
Just mentioned this story to my fisherman friend and he said he has dug quite a few ponds and often seen fish magically appear before they stock the pond.
There is debate about whether Zelandia the mostly submerged continent under New Zealand was ever fully submerged. One of the arguments agains this is the existence of related species of fresh water fish in NZ and New Caledonia. I guess this means there is the possibility that so long as some lake somewhere didn't submerge, the fish could have re-populated to newly rising islands.