Context of "Register a total of 1 unique item in the Asgarnia and Misthalin section of your Slayer collection log" 8W9W

Well done. You got yourself your first collection log item. On your journey you will eventually complete the Slayer collection log. Goblins and Chickens drop slayer log uniques. Therefore, you can only kill them, if your task is to obtain a unique for the "Asgarnia and Misthalin slayer collection log", OR you've obtained all of their uniques (see rule 2.E2). This time, you didn't have to level up your Slayer, but rule 9.19.1.E1 states, that you may go for any item in the dropdown, as long as you follow the rest of the rules in 9.19. This also means levelling up Slayer. The slayer rules are comprehensive, so have a look whenever you roll a slayer log task.