County stickers have to do with county-collected personal property taxes and are not related to the tags, which are state-issued with state-collected vehicle registration fees.
See this page for info on how to get the sticker:
http://www.fairfaxcounty.gov/dta/vehicle_decals.htm
and from the FAQ located at
http://www.fairfaxcounty.gov/dta/vd_renew_faq.htm :
"If you are new to Fairfax County or purchase a new vehicle, you have 60 days from the date the vehicle was moved into the County to obtain and display a decal."