Hi Catherine,
It’s best to just throw the egg away. It is highly unlikely to be fertile. It’s not a good idea to breed different species, creating a hybrid. It’s also very hard to breed cockatoos or house males and female together. In the wild, they split up after each breeding season. In captivity, if the male cockatoos are not separated from the females most of the year, the male gets aggressive and kills the females. Since you have already had a warning from the Corella, do not cage him with the female again or risk having her horribly injured or killed. As for eggs, take those away and try making some changes to keep her from egg laying. When you handle her, you need to limit petting to her head. When you pet a bird on the body, this sends the message that you are the mate and it triggers their hormones. Don’t let her have anything she can use as a nest – no boxes or bird huts, nothing she can get inside of. Don’t let her shred paper or cardboard. If she tries to sit in a corner of the cage, block the area by hanging some toys there. When she is out of the cage, don’t let her get in dark cozy places. Rearrange her toys often and move her cage to other places in the room. Also limit her light to 8-10 hours a day by covering her cage early each evening. You don’t want her to turn into a chronic egg layer or you will have to take her to an avian vet for a hormone implant or shot.
Thank you for asking Lafeber,
Brenda