Exactly right!
Dunno if this is possible but I can certainly ask Hoofmaster about it. However, I'd want to make sure it rerolls as another DQ of that Rarity to stop people trying to get a better rarity.
I would pay a few fsp if needed to reroll my Daily Quests if I had the chance! . Possibly even every day I got one with a current stamina reward.. Lol