The link is to last years event as they haven't added it to the site events but it has been confirmed on their facebook page
https://www.facebook.com/PerthZoo/
This is a pretty standard thing a lot of zoos do yearly around Australia. So its worthwhile contacting your local one to see if they have a similar deal.
Updated on site:
http://perthzoo.wa.gov.au/calendar/fathers-day-2/
How do they know your a dad?
Paternity tests?