These ones are unfortunately NOT for the 'Impressions' quest. The only cockatrices that exist in TT are the 'Stonegazer' ones.
If you did a search for 'petrifier cockatrice' after looking up that quest like I did, the only one that shows up is this entry and not 'a petrifier cockatrice' which is the the correct one.
If you click on the mob link on the quest screen itself, it'll point you to the correct 'a petrifier cockatrice' located in the Dreadlands.
Why both don't show up when you do a search for 'petrifier cockatrice', I don't know since both contain that string.
Anyways, save yourself a couple of hours of travelling, headbashing, and headache and make your way over to the Dreadlands to hunt the correct bird.
Edited, Jan 13th 2019 9:00pm by Kyrros