Does this pigeon deserve to die?

With all the trouble Australia has had with introduced species, I don't blame them whatsoever for being overly cautious even if it is just a pigeon.

Ideally you'd send it back, but I'm not sure the costs outweigh the benefit.
I worked with a pigeon fancier and he used to bring a magazine to work that had adverts for pigeons for sale. As with many small ads they were full of abbreviations the most common of which was W/F. One of the lads asked if it meant 'with feathers' :D .................... "no you daft buggers it means white flights!"