Few mistake's i made before i figured it out. Make sure to accept the quest in discord first, Make sure your streaming the game and not just your screen and make sure to get your pet claim code in discord and enter in in bnet after your done.
Here's the YouTube guide i used (not me, no affiliation)
https://www.youtube.com/watch?v=mPElA5LAOZQ
Step by step guide taken from wowhead comments
For those who'd like step by step instructions (like me, had no clue where the quests were!)
^ On the desktop app,
1.Left side where the server icons are, scroll to bottom and click 'Explore discoverable servers'
2.Click on 'Quests'
3.Click 'Accept Quest'
4.Stream in any channel or a dm
make sure you are sharing the game not just the screen!
edit: It does not appear to count time until after you accept the quest.