Do you mean you finished your first one today or you started it? Upon opening, you get I think 9 days of one quest a day. But you won't be able to open another cookie until the first one runs out. I use them frequently, when you have less than 24 hours left it will tell you what time it will run out. After that, you can use another one.
edit- at the top of the faerie quests page where you accept each quest. That's where it will tell you how long you have left.