I have had cats whose birthdays were known to me because I watched their mother give birth to them (my beloved Mao was one) on 2 March 1991.
My current two, Tina & Leon, I only have an approximate date of 15 March 2010.
And others (Bubeleh, Heidi, Lucky, D.D., Geisel, Graham, etc.) I had no idea at all.