You should replace quick-thread-forum with the actual url of the forum where you want your users to be redirected to after they click the newly added button.
The language is hard coded. if you don't mind a bit of extra work replace Quick thread with {{ phrase('quick_thread') }} and then create the quick_thread phrase. To make it even better you can make this a template modification so there will be no manual edits. I hope it helps you.
I just double checked it is the forum_list template I want to add the entire quick reply to and to direct it to forum #2
Reason
The site has no forum_index visible, only forum_list which mixed together the threads of two forums.
Therefore there is no quick thread on that template but I wish to add it directing the quick thread to forum #2.
This NEW site is quite unusual
No Index page
No buttons
It strips out a lot of forum looking stuff and consists of one page forum_list only and because there is no NEW THREAD button I want Quick Thread only but to direct to forum 2 because the only other forum needs special permission to post.
So basically the forum_list template shows the thread of two forums but I need a quick reply to be added directing it to post into a specific forum.