Yep, I did the quest before 3am server reset.
I re-logged, and also disabled all my addons but he's not giving me the quest. Nor are the other Master Tamers like Grand Master Lydia Accoste or Stone Cold Trixxy.
I saw a post on the offical forums from 2012 about some people having trouble with Pet Battle daily resets, but it was locked.
I've also seen some posts on Wowhead how some people can only complete this quest once a month
I've submitted a bug report... but I have a feeling I won't be able to get a reply before the Faire ends :'(