While I was offline, for New Year's Eve, I had to cook and peel about 50 Quail Eggs. I'll give you what I learned:
Boil for 5 minutes, then drain and submerge in an ice-bath to stop the cooking. This will result in perfectly cooked eggs with no green "tinge" to the yolk (a sign of over-cooking).
Quail eggs also suffer from the freshness problem that chicken eggs do when boiled. FRESH Quail eggs are really, really, hard to peel, just like fresh chicken eggs. Buy your Quail eggs a week or two in advance, then boil/peel them.
Peeling tip (I use this on Chicken eggs all the time, and it works for Quail eggs as well)
Take the blunt end of the egg, where the air pocket is located, and gently smash the shell against a cutting board. While the shell is pressed into the air pocket, roll the onto it's side, all the way to the sharper end of the egg, breaking the shell all the way. Carefully roll the egg front and back, pressing down lightly, to break the shell completely around the egg, but not hard enough to crush the egg white. Start peeling the shell at the air pocket. Many times, I've been able to peel the entire egg in one continuous strip.
I did 50 quail eggs in about 20 minutes or so.
Peace, Love, and Vegetable Rights!
Eat Meat and Save the Plants!