The Birth Records tab is a dependant tab of Dogs (Dame and Sire). You cannot create a Reproduction Management record without relating it to a Dame and a Sire record. Even if the Dame or Sire is not part of your organization, you should still create a dog record with the Breeder record type and set the Status to Non-Organization Breeder.
It is best to create birth records from the Birth stage of a Reproduction Management record if you have all of the Heat, Mating, Gestation and Whelping records. Otherwise, you can create Birth Records records from it's tab or the dog's record (Breeder record types only) using related lists. Filling it out from the Dame's or Sire's record will auto-fill the Dame or Sire field.
There are no Record Types included for Birth Records.