As bear says, you need to level you bird up to rank 40, then you can retire it for breeding. Each generation can advance pedigree by 1. As pedigree goes up, the XP needed to progress to the next pedigree increases too.

In all - presently, it takes about 1,500 to 2,000 races to reach pedigree 9. Though this number will likely drop significantly as of tommorow since they're boosting XP gains in racing. At any rate it's not something that'll happen overnight