What makes you think such would ever get issued? Employment authorization for dependents of A-1 visa holders is limited (pretty much working for your own embassy/mission). It also depends on what country you are coming from (as the eligibility is determined on reciprocity with the home country's rules for US diplomats and their families).
Best to consult an attorney.
Anyhow if you qualify, times can push 90 days. It depends on the situation and which office you've submitted the application to. Time estimates can be had at this site: https://egov.uscis.gov/cris/processTimesDisplayInit.do

