"Birthdate" as a compound word is more common on official forms and in writing. Birth date may be the way that it is spoken by most English speakers, who rarely use it as a compound word. If its usage is for a database then it would be best to stick with using "birthdate", the compound word.
Chaldean Numerology: Discover Love and Relationship Compatibility: By Sanya Singh Can your name or birthdate predict the future of your love life? Chaldean numerology and love numerology suggest that ...