Depending on how long the dead docket has been in place, you may be able to get the case dismissed. Criminal defendants have certain constitutional rights to a speedy trial that cannot be ignored simply by placing a case on the "Dead Docket." Since this case is affecting your employment status, you may be able to successfully get the case dismissed with prejudice (meaning it could never be brought again). However, in Georgia it is unlikely that the case would ever be expunged.
A Dead Docket means the case is still open and that is why you cannot get the case expunged. You need to contact an experienced criminal defense attorney to discuss your options to resolve your case.