Full drivers license if definitely a problem after 2014 when Florida adopted the new definition of "Personal Information" at Fla. Stat. 501.171.  I can't comment whether sharing the birthday without more may be a separate violation of your company's privacy policy. 

Here's the statute:

501.171 Security of confidential personal information.—

(1) DEFINITIONS.—As used in this section, the term:

(g)1. “Personal information” means either of the following:

a. An individual’s first name or first initial and last name in combination with any one or more of the following data elements for that individual:

(I) A social security number;

(II) A driver license or identification card number, passport number, military identification number, or other similar number issued on a government document used to verify identity;