Yes quail eggs do expire.
Just like chicken eggs the quail eggs also have a shelf life and should not be eaten after they have passed the use by date.
Quail Eggs will last for up to 6 weeks in the refrigerator.
If you leave the quail eggs out at room temperature the quail eggs will only last up to 4 weeks.
So make sure to refrigerate the quail eggs if you want to keep the quail eggs longer than 4 weeks or eat them before the 4 weeks.
But if you have left the quail eggs out at room temperature longer than 4 weeks then they are likely bad and should not be eaten.