Quack's Hut can be found on Forest Island.
From the large tree, you should be able to see some small huts just across the water. From here, go down one level to another bunch of huts. Quack's Hut can be found on this level. Just click on it, and if Quack the Duck comes out, it's the correct hut. Then, wait for Quack to go back in and open the door again. You need to open this door a total of 3 times to earn the achievement.
I am not sure if this one is technically MISSABLE, since Quack ends up joining you on your adventure after this island.