You're contradicting yourself, how can it be unique if only 1000 can be assigned per given date of birth? What if more than one thousand babies are born in the country one day?
It's the same in Sweden: YYYY-MM-DD-XXXX is the format for a personnummer, double the population of Denmark and there are no collisions.
Thanks for correcting it :)
edit: I was wrong. Wikipedia says, “The first digit of the sequence number encodes the century of birth (so that centenarians are distinguished from infants)”.
It also says “the last digit of the sequence number is odd for males and even for females”. What a strange system. Essentially the last three digits are two different sequences made to look like one.